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The stability of bound chlorides in cement paste with sulfate attackJian Geng a ,b ,⁎,Dave Easterbrook b ,Long-yuan Li b ,Li-wei Mo aa Research Center of Green Building Materials and Waste Resources Reuse,Ningbo Institute of Technology,Zhejiang University,China bSchool of Marine Science and Engineering,University of Plymouth,UKa b s t r a c ta r t i c l e i n f o Article history:Received 10July 2014Accepted 25November 2014Available online 27December 2014Keywords:Sulfate attack (C)Bound chlorides (D)Stability (C)Fly ash (D)Ground granulated blast-furnace slag (D)This paper presents an experimental investigation on the stability of bound chlorides in chloride-contaminated cement pastes with and without FA/GGBS when subjected to Na 2SO 4and MgSO 4attack.It is shown that bound chlorides were released in the chloride-contaminated pastes when exposed to Na 2SO 4or MgSO 4solution.This is mainly attributed to the decomposition of Friedel's salt (FS),where Cl −bound in FS is replaced by SO 42−.How-ever there were fewer released chlorides found in the pastes exposed to MgSO 4solution than in those exposed to Na 2SO 4solution.This is partly due to the low pH in the pore solution and partly due to the blocking effect of brucite on ionic transport caused by MgSO 4.The inclusion of FA/GGBS in concrete can increase the decomposition of FS and thus the release of bound chlorides.However,it also resists the penetration of Na 2SO 4and thus reduces the attack of Na 2SO 4.©2014Elsevier Ltd.All rights reserved.1.IntroductionThe corrosion of reinforcing steel in concrete structures,due to chlo-ride ion contamination,is one of the main reasons for the deterioration of concrete structures.There are two forms of chloride ions in concrete.One is free chlorides and the other is bound chlorides.It is well-known that the corrosion of reinforcing steel is mainly induced by the free chlo-rides,so reducing free chlorides by increasing bound chlorides will be bene ﬁcial to the durability of concrete structures.According to the bind-ing mechanism,chloride ions can be bound through chemical reactions and physical absorption.In the former,chloride ions are mainly bound in Friedel's salt (FS)(3CaO·Al 2O 3·CaCl 2·10H 2O)through hydration reactions between chloride ions,tricalcium aluminate (C 3A)and its hydration products.In the latter,chloride ions are mainly absorbed by calcium silicate hydrate (C –S –H gel).It was reported that the formation of bound chlorides could be affected by a multitude of factors such as the quantity of C 3A in cement,supplementary cementitious materials (SCM),alkalinity of pore solution,Ca/Si and Ca/Al of hydration products,chloride salt type,and service condition of concrete structures [1–5].In summary,the chloride binding capacity of concrete can be improved by using SCM or cement with high C 3A content.However,many researchers have identi ﬁed that the stability of bound chlorides,espe-cially of FS,can be affected by pH,carbonation,and chemical erosion [6–9].Sulfate attack is another problem for the durability of concrete struc-tures.The attack of sodium sulfate (Na 2SO 4)and magnesium sulfate (MgSO 4)on concrete is a common phenomenon.The mechanisms of Na 2SO 4and MgSO 4attack on concrete are different,mainly due to the solubility of phases formed with sodium and magnesium ions [10–12].With regard to Na 2SO 4attack,the deterioration of concrete is attributed to the formation of expansion products such as gypsum (CaSO 4·2H 2O)and secondary ettringite (AFt)(3CaO·Al 2O 3·3CaSO 4·32H 2O)according to the following equations:Ca ðOH Þ2þNa 2SO 4þ2H 2O →CaSO 4·2H 2O þ2NaOHð1Þ3ðCaSO 4·2H 2O Þþ3CaO ·Al 2O 3þ26H 2O →3CaO ·Al 2O 3·3CaSO 4·32H 2Oð2Þ2ðCaSO 4·2H 2O Þþ3CaO ·Al 2O 3·CaSO 4·12H 2O þ16H 2O →3CaO ·Al 2O 3·3CaSO 4·32H 2O :ð3ÞWhereas for MgSO 4attack,the transformation of the cementitious C –S –H gel to the non-cementitious magnesium silicate hydrate mush (M –S –H),which has very little strength,is the main reason for the dete-rioration of concrete,although gypsum and secondary AFt are also formed during the attack.In addition,brucite,i.e.Mg(OH)2,will form when magnesium is present in the pore solution,which has low solubil-ity and could densify the pore system and thus affect the transport ofCement and Concrete Research 68(2015)211–222⁎Corresponding author.E-mail address:gengjian@ (J.Geng)./10.1016/j.cemconres.2014.11.0100008-8846/©2014Elsevier Ltd.All rightsreserved.Contents lists available at ScienceDirectCement and Concrete Researchj o u rn a l h o m e p a g e :h t tp ://e e s.e l s e v i e r.c o m /C EM C O N /d e f a u l t.a s pions in the cement paste.The mechanism of MgSO4attack occurs according to the following equations:CaðOHÞ2þMgSO4þ2H2O→CaSO4·2H2OþMgðOHÞ2ð4Þx CaO·y SiO2·z H2Oþx MgSO4þð3xþ0:5y−zÞH2O→xðCaSO4·2H2OÞþx MgðOHÞ2þ0:5yð2SiO2·H2OÞð5Þ4MgðOHÞ2þSiO2·nH2O→4MgO·SiO2·8:5H2Oþðn−4:5ÞH2O:ð6ÞIn fact,sulfate attack and chloride contamination are often found to coexist in concrete structures which are exposed to marine and saline environments.The effects of the sulfate and chloride on a concrete structure's durability are multifaceted.On the one hand,the existence of sulfate,especially of Na2SO4,inhibits the formation of FS and reduces the quantity of bound chlorides[13–15].On the other hand,the exis-tence of chloride ions is beneﬁcial for the resistance of concrete to Na2SO4and MgSO4attack[15–18].However,Baghabra argued that the effect of chloride ions on MgSO4attack was slight because the trans-formation of cementitious C–S–H gel to non-cementitious M–S–H was not affected by chloride ions[19].Despite the work on the interaction of sulfate and chloride in con-crete mentioned above,there is very little work on the effect of sulfate attack on the stability of bound chlorides in concrete.Brown and Badger investigated the distributions of bound sulfates and chlorides inﬁeld concrete cores exposed to mixed NaCl,Na2SO4and MgSO4attack. They found that there was extensive AFt in the absence of a gypsum zone for some concrete cores[20].Xu et al.obtained similar results, i.e.that sulfate attack could lead to the release of bound chlorides[21]. Both studies suggested the transformation of FS to AFt due to sulfate attack,but the mechanism of FS transform to AFt and the stability of bound chlorides absorbed by C–S–H gel under sulfate attack were not discussed in depth.It is well known that the use ofﬂy ash(FA)and ground granulated blast-furnace slag(GGBS)in concrete can not only improve the chloride binding capacity of concrete,but also the resistance of concrete to sulfate attack[22,23].Hence,it would be interesting to know how they affect the stability of bound chlorides when the concrete is under sulfate attack.The purpose of this paper is to report the experimental in-vestigation on the stability of bound chlorides in cement paste under Na2SO4and MgSO4attack,and the corresponding inﬂuence of FA and GGBS on the stability of bound chlorides.The stability of bound chlorides in cement paste was examined by analyzing the change of a dimensionless index,R cl,which represents the mass ratio of bound chlo-rides to initial total chlorides in the sample after it was exposed to a5% Na2SO4solution or a5%MgSO4solution for28,56or90days.The mech-anisms of the release of bound chlorides are discussed based on the results of X-ray diffraction(XRD),Fourier transform infrared(FT-IR) and differential thermo-gravimetric analysis(DTG).2.Experiment2.1.MaterialsThe materials used in the experiments were Type42.5Ordinary Portland Cement(OPC),grade II FA and GGBS.The chemical composi-tions of OPC,FA and GGBS are listed in Table1.The potential phase com-positions of OPC,calculated from chemical analysis by Bogue,are given in Table2.All other chemical reagents used in the experiments,but not listed in the tables,are analytically pure.2.2.MethodsIn order to reduce the experimental running time but still able to achieve good and representative results,chloride binding was achieved by using0.5mol/L NaCl solution as the mixing water for the casting of samples.The mass ratio of the mixing water to the binder(cement and SCM)was0.5,which was the same for all samples.The inﬂuence of single and combined use of FA and GGBS on the stability of bound chlorides was also investigated.The replacement of cement with SCM was30%by weight,and the proportions of FA to GGBS in the combined samples were either1:1or7:3.The detailed mix proportions of the samples tested are listed in Table3.A total of106samples were tested.All samples were of a size of 40mm×40mm×160mm.There were three groups of samples.The ﬁrst group(2×5×7samples)were cured at a standard curing condi-tion(20±2°C and95%RH)for periods of1,3,7,14,28,56and90days for the investigation of the effect of curing time and SCM on the evolu-tion of bound chlorides in the cement paste.The second group(2×5×3 samples)were examined for the effect of Na2SO4attack on the stability of bound chlorides.In this group,all samples,after the56days standard curing,were dried at a room temperature(20±2°C and60%RH)for 1day.Then,for each sample itsﬁve surfaces were sealed by parafﬁn wax and one40mm×40mm surface was left untouched.After then, all samples were immersed in a covered plastic container(575mm ×400mm×275mm)of5%Na2SO4solution for28,56and90days at the standard curing condition(20±2°C and95%RH).The third group(2×1×3samples)were for the samples only with OPC,which were cured as the same as those done in the second group.The only dif-ference is that they were immersed in a similar covered container of5% MgSO4solution for28,56and90days at the standard curing condition (20±2°C and95%RH)for the examination of the effect of MgSO4at-tack on the stability of bound chlorides.The volume of the sulfate solu-tions used in the immersion tests was25L and the storage solutions were not renewed during the immersed tests.In the second and third groups,when the attack time reached28,56, and90days,the samples were dried at room temperature for1day,and then were sliced into four pieces parallel to the exposed surface (starting from the exposed surface)and each piece is one cm thick. Afterwards,each piece was broken into small blocks,which were then immersed in anhydrous ethanol for7days to terminate hydration. These small blocks were ground intoﬁne powder by passing through a sieve of0.15mm mesh aperture size,which was then stored in a des-iccator with silica gel and soda lime at11%RH to minimize carbonation before it was used in the tests for chloride content titration and other material characterization analyses.The initial total chloride content(C t)of the sample cured at the stan-dard curing condition can be calculated based on the mixing water of Table1Chemical composition of main materials(data presented by mass%).SiO2CaO MgO Fe2O3Al2O3SO3Ignition loss OPC19.6760.43 4.56 4.20 5.70 2.30 2.54FA43.10 6.300.247.2638.200.70 2.04GGBS23.5052.80 6.500.7011.80 1.650.78Table2Potential phase composition of OPC(data presented by mass%).Potential phase composition OPCC3S51.58C2S17.77C3A8.01C4AF12.773.91212J.Geng et al./Cement and Concrete Research68(2015)211–2220.5mol/L NaCl solution,which is 8.863mg ·g −1.The free chloride content (C f )was measured using the traditional leaching method according to the standard of Test Code for Hydraulic Concrete (SL352-2006)and the total chloride content (C t )was measured using the acid-soluble method (SL352-2006).In order to analyze the stability of bound chlorides in concrete,the dimensionless index (R cl )was exam-ined,which is de ﬁned as follows,R cl ¼C t −C f %ð7Þwhere 8.863mg.g −1is the initial total chloride content in the sample.X-ray diffraction (XRD)/reference intensity ratio (RIR)analysis and DTG can be used to approximately determine the quantity of FS,AFt and calcium hydroxide (CH)in the samples.XRD/RIR can determine the relative mass relations among different minerals in a sample,which is calculated according to the following equations [24,25]:W i ¼I i =RIR iX i ¼1I i=RIR i ðÞð8ÞW 1þW 2þW 3þ⋯þW l ¼1ð9Þwhere W i is the relative mass of mineral i ,RIR i is the reference intensityratio of mineral i ,which can be collected from the PDF card of the Inter-national Centre for Diffraction Data (ICDD),I i is the integral intensity of the highest peak of mineral i ,which is calculated using X'Pert HighScore Plus ™software,and N is the number of minerals in the sample.XRD/RIR is usually used to determine the quantity of substances in metals because of simple compositions [25].For cement based materials,it is rather complicated to accurately determine the kinds of hydration products,which increases the dif ﬁculty of the quantitative analysis.However,if the quantity of one of the minerals can be determinedusing other methods,the calculation process of XRD/RIR becomes pared with the FS and AFt,the quantity of CH can be accurately determined using DTG.Therefore,the quantities of the FS and AFt can be calculated by solving the following algebraic equations,m FS :m AFt ¼T 1ð10Þm FSFS þm AFt þm CH ¼T 2ð11Þm AFtm FS þm AFt þm CH ¼T 3ð12Þm CHm FS þm AFt þm CH¼T 4ð13Þwhere m FS ,m AFt and m CH are masses of FS,AFt and CH,respectively,T 1,T 2,T 3and T 4are the mass ratios,which can be calculated from Eqs.(8)and (9).Note that,m CH can be determined by DTG and thus m FS and m AFt can be determined by Eq.(10)plus any one taken from Eqs.(11)–(13).XRD was carried out using the D8Advance instrument of Bruker AXS with a Cu K αradiation generated with 40kV and 30mA.The diffraction spectra were collected in the range of 5–60°(2θ)scale,with a step sizeTable 3Mix proportions (data presented by mass %).Samples OPC FA GGBS w/b a NoteCN 100000.5Exposed to 5%Na 2SO 4solutionCF 703000.5CG 700300.5CF1G17015150.5CF7G3702190.5CM1000.5Exposed to 5%MgSO 4solutionaw/b represents the mass ratio of mixing water (i.e.0.5mol/L NaCl solution)to binder (cement +SCM).Fig.1.Variation of R cl with standard curing time in samples of differentmixes.Fig.2.Values of R cl in the surface layer of the sample at various different sulfate attack times (CM was exposed to MgSO 4,while all the others were exposed to Na 2SO 4).Fig.3.Values of R cl in different layers of the sample after 90days sulfate attack (1st layer is next to the surface and 4th layer is away from the surface.CM was exposed to MgSO 4,while all the others were exposed to Na 2SO 4).213J.Geng et al./Cement and Concrete Research 68(2015)211–222of 0.02°/s.FT-IR was performed for the samples on a Nicolet Nexus 470spectrometer using the KBr pellet technique in the range of 400–4000cm −1.DTG was carried out in a Netzsch TG-209F1thermal an-alyzer,using a heating rate of 20°C/min at the range of 25–1000°C,in N 2atmosphere.3.Stability of bound chlorides 3.1.Standard curing conditionThe variation of R cl during the standard curing time is shown in Fig.1.It can be seen from the ﬁgure that R cl in the samples with SCM is higher than that in the sample only with OPC when they have the same curing time,which is more obvious after the curing time exceeds 14days.Up to 28days,the combined use of FA and GGBS results in higher values of R cl in CF1G1and CF7G3than in the samples with only either FA (CF)or GGBS (CG).However,after the 28days standard curing,the R cl value of the samples has an order of CF ≈CF7G3N CF1G1N CG,which increases with the increased proportion of FA to GGBS.The latereffect of FA on chloride binding is mainly due to its slow pozzolanic re-action.The results shown in Fig.1indicate that the inclusion of SCM in concrete can increase the chloride binding capacity and the effect of FA on chloride binding is more signi ﬁcant than that of GGBS.Furthermore,they also show that the R cl values of all samples increase very obviously before 28days but after that there is less change,suggesting that the equilibrium between free and bound chlorides has been reached.3.2.Sulfate attack conditionFig.2shows the expected decrease in R cl of the surface layer of all samples with the sulfate attack,but the rate of the decrease is higher than that was reported [21].The R cl value in the surface layer of sample CN exposed to Na 2SO 4solution,for example,decreases from 59.8%to 4.3%after only 28days.After that,R cl continuously decreases with the attack time but with a slow reduction rate,from 4.3%at 28days to 1.9%at 90days.The results for locations other than the surface layer at 90days are shown in Fig.3.It can be seen from the ﬁgure that,although the 4th layer of sample CN is far away from theexposedFig.4.XRD patterns of samples CN(CM),CF and CG at standard curing condition for (A)28and (B)56days (E:ettringite (AFt),F:Friedel's salt (FS),CH:calcium hydroxide,M:mono-sulfoaluminate,V:Vaterite,CSH:C –S –H gel,C:calcite).214J.Geng et al./Cement and Concrete Research 68(2015)211–222surface,there is still a notable decrease in the R cl value from59.8%at the beginning of the Na2SO4attack to16.6%after90days of attack.This demonstrates that the stability of bound chlorides in concrete is very susceptible to Na2SO4attack.Note that the data plotted in Fig.2show that there is also a decrease in the R cl values of the samples with SCM after Na2SO4attack for28days, but the R cl values are still higher than that of the sample CN only with OPC.This suggests that the use of SCM can alleviate the effect of Na2SO4attack on the stability of bound chlorides.This is partly because the effect of SCM on the diffusion of ions,since the ionic diffusion coef-ﬁcient in cement paste with SCM is normally lower than that in OPC paste,and partly because the cement paste with SCM has more bound chlorides[26].Additionally,in contrast with the results obtained under the standard curing condition,the R cl values of the samples with SCM increase with the decreased proportion of FA to GGBS,and also the R cl value of the surface layer of sample CF is the lowest of all samples containing SCM,following the Na2SO4attack.This suggests that Na2SO4attack can also alter the effect of SCM on the stability of bound chlorides.This appears to be consistent with what is reported in literature[21].The stability of bound chlorides in concrete under MgSO4attack is also shown in Figs.2and3.When the MgSO4attack time extends from0to28days,the R cl value of the surface layer of sample CM decreases from59.8%to26.3%,which is slower than that of sample CN exposed to Na2SO4solution.When the attack time reaches90days, the R cl value of sample CM's surface layer decreases to7.5%,which is still almost four times as high as that of sample CN.This indicates that the stability of bound chlorides is less susceptible to MgSO4attack when compared with Na2SO4attack.Again,thisﬁnding is consistent with what is reported in other experiments[21,27].The different reductions of R cl in samples CM and CN reﬂect the different effects of MgSO4and Na2SO4on bound chlorides.During the immersion process free chloride ions will diffuse out and sulfate ions will diffuse into the specimen.The former may decrease the bound chlo-ride level in the sample owing to the equilibrium between the free and bound chlorides.The latter can transform FS into AFt,which not only can reduce the bound chlorides but also can change the pore system and thus affect the diffusion rate of ions.In addition,when magnesium is present,brucite will be formed,which can also change the pore sys-tem and thus affect the transport of ions and the R cl value.The slower reduction of R cl found in sample CM shown in Figs.2and3indicates that the magnesium ions must have some inﬂuence on the sulfate attack to the bound chlorides.This inﬂuence could be physical and/or chemi-cal.The former is mainly due to the forming of brucite in the surface layer,which reduces the inward diffusion of sulfate ions and the out-ward diffusion of chloride ions.Indeed,the measured free chloride con-centration after the90days immersion was found to be higher in sample CM than in sample CN and have the ratios of about1:0.72for the surface layer and1:0.81for the4th layer.An accurate analysis for the diffusion effect on the bound chlorides requires having more data on thinner layers and knowing the binding isotherms.Nevertheless, the above results did indicate that the diffusion of chloride ions was affected by magnesium ions.The chemical effect of magnesium ions on bound chlorides will be discussed in the next section.Note that the ionic diffusion coefﬁcient in concrete with SCM is nor-mally smaller than that in concrete only with OPC.Thus,the inclusion of SCM in cement paste can provide additional resistance to the ingress of sulfate ions,which in turn can affect the stability of bound chlorides. More discussion on this will be provided in the next section.4.Material characterization analyses4.1.X-ray diffractionThe XRD patterns of samples CN,CF and CG cured at the standard curing condition for28and56days are shown in Fig.4.From the XRD patterns one can identify the FS with a very obvious diffraction peak at around11°2θ.Fig.5shows the relative masses of AFt,FS and CH in samples CN,CF and CG after they were cured in the standard condition for56days.It can be seen from theﬁgure that the use of FA and GGBS is beneﬁcial to forming more FS.This result can be attributed to two rea-sons.First,the forming process of FS in concrete has been associated with the quantity of aluminate in cementious materials.The higher the quantity of aluminate,the more FS is formed.According to the chemical composition shown in Table1,there is a larger quantity of alu-minate in GGBS and FA than in OPC,which can be released due to the latent hydraulic property of GGBS and the pozzolanic property of FA, which is beneﬁcial to the formation of FS.Secondly,the formation of FS would be hindered because SO42−can react with aluminate prior to Cl−to form mono-sulfoaluminate(AFm)and AFt[13–15].In addition, C–A–H and C–S–H gel,formed due to the hydration reactions induced by FA and GGBS,are also beneﬁcial to chloride binding.As shown in Fig.5,although the quantity of aluminate in FA is higher than that in GGBS,the quantity of FS in sample CF is still lower than that in sample CG after standard curing for56days.It was believed that only reactive alumina Al2O3r−in SCM could react with Cl−to form FS[5].The quantity of CaO in FA used in this study is6.3%,which is low calciumﬂy ash according to Chinese speciﬁcation GB/T15696-2005,and where Mullite is the main form of Al2O3,so it is adverse to the formation of FS.Nevertheless,a notable decrease in the intensity of diffraction peak (IDP)of CH can be found in the XRD patterns of sample CF over the curing time from28to56days,which is induced due to the pozzolanic reaction between CH and FA.As a result,more C–S–H gel and C–A–H are formed,which could increase the bound chlorides in sample CF.It should be noticed that the IDP change at around30°(2θ)shown in Fig.4correlates with both C–S–H gel and calcite(CaCO3),because of the overlap of the two strongest diffraction peaks at29.25°(2θ)and 29.40°2θ,respectively[8,28].The XRD patterns of sample CN under Na2SO4attack are shown in Fig.6.It can be observed from Fig.6A that the IDP of FS in the surface layer of sample CN becomes very weak after Na2SO4attack for28 days,which indicates that FS has been decomposed due to the Na2SO4 attack.A quantitative analysis of FS,AFt and CH of sample CN after the Na2SO4attack for28and90days is shown in Fig.7.It can be seen from theﬁgure that the relative mass of FS in the sample decreases very quickly from2.04to0.45after the28days attack.This suggests that the stability of FS is very susceptible to Na2SO4attack,which may also explain why the decrease of R cl is quick as is shown in Fig.2.How-ever,when the attack time is extended from28to90days,the change in the quantity of FS is slight,which indicates that a large quantity of FShasFig.5.Analysis of ettringite(AFt),Friedel's salt(FS)and calcium hydroxide(CH)in sam-ples CN/CM,CF and CG after they had56days standard curing(wt.%represents the mass percentage of AFt/FS/CH in sample).215J.Geng et al./Cement and Concrete Research68(2015)211–222been decomposed following 28days of the Na 2SO 4attack.Moreover,it can be seen from Fig.7that the quantity of FS gradually decreases from the inside to the surface,which correlates with the change of the R cl value shown in Fig.3.In addition,one can see from Fig.6B that AFt with a diffraction peak at around 9°(2θ)can be detected in every layer of sample CN after the Na 2SO 4attack for 90days.The data shown in Fig.7for AFt indicate that the quantity of AFt in the fourth layer of sam-ple CN is higher than its initial value,which con ﬁrms that the attack of Na 2SO 4has reached the fourth layer of the sample.Fig.7also shows the expected opposite changes of FS and AFt with time.The XRD patterns of samples CF and CG after the Na 2SO 4attack for 90days are shown in Fig.8.Similar to the sample CN,the diffraction peaks of FS in the samples with SCM,especially in sample CF,become very weak.Similar to the analysis of the sample CN,Fig.9shows the relative mass of FS,AFt and CH of samples CF and CG after the Na 2SO 4attack for 90days.It seems that the quantities of FS in samples CF and CG are as high as that in sample CN after the Na 2SO 4attack.However,considering the higher quantity of FS in samples CF and CG before the Na 2SO 4attack as shown in Fig.5,the decrease of the quantity of FS in them is quicker than that in sample CN.Therefore,it can be concluded that the stability of FS in the samples with FA or GGBS is susceptible to Na 2SO 4attack when compared to the sample CN.The XRD patterns of samples CN and CM attacked by Na 2SO 4and MgSO 4for 90days are shown in Fig.10.An interesting ﬁnding is that there is still an obvious diffraction peak of FS in the sample CM,which is different from the sample CN attacked by Na 2SO 4.The analysis results shown in Fig.11demonstrate that there is more FS in sample CM than in sample CN.Therefore,it can be concluded that the Na 2SO 4attack has more effect on the decomposition of FS in hardened cement paste than the MgSO 4attack.In addition,the IDP of AFt in sample CM is lower than that in sample CN due to the different erosion mechanisms.However,there is still an obvious increase in AFt for sample CM from 0to 90days as demonstrated in Figs.5and 11,which indicates that MgSO 4attack can also lead to the formation of secondary AFt.NoteFig.6.XRD patterns of samples CN with Na 2SO 4attack.(A)1st layer at different days and (B)different layers at 90days (E:ettringite (AFt),F:Friedel's salt (FS),CH:calcium hydroxide,M:mono-sulfoaluminate,V:Vaterite,CSH:C –S –H gel,C:calcite).216J.Geng et al./Cement and Concrete Research 68(2015)211–222that,when magnesium is included in the exposure solution,brucite is formed at the expense of calcium hydroxide,which can affect not only the leaching of chloride from the specimen but also the inward trans-port of sulfate from the exposed solution and thus provide the in ﬂuence on the decomposition of FS and the formation of AFt.However,our XRD result did not reveal a signi ﬁcant amount of brucite and/or gypsum in the surface layer.This is probably due to the specimen layer used in the tests being too thick.Both Skaropoulou and Sotiriadis reported their test results in which brucite was detected in XRD patterns,but the IDP of it was very weak when compared to other phases [11,17].However,in other similar experiments brucite was not detected in XRD patterns [27,29,30].This is probably attributed to the consumption of brucite due to the formation of M –S –H as shown in Eqs.(4)–(6)[19].4.2.Fourier transform infrared (FT-IR)Fig.12shows the FT-IR spectra of sample CN after the Na 2SO 4attack for 28and 90days,respectively.The band at around 3640cm −1is due to the stretching vibration of \OH in Ca(OH)2[30],which is very weak in all samples due to Na 2SO 4attack.The presence of carbonate bands at around 1430and 870cm −1indicates that the samples have already absorbed CO 2molecules from the air before they were immersed into sulfate solution [31].The band at around 1110cm −1comes from asym-metric stretching vibration of S –O in SO 42−,which is identi ﬁed as the ﬁngerprint peak of AFt [32,33].As is shown in Fig.12,owing to more secondary AFt being formed,this band becomes stronger from the in-side to the surface over the attack time.The changes in the bands at around 3440and 1650cm −1are due to the stretching vibration of \OH in structural water of hydration products and the bending vibra-tion of \OH in the interlayer water of hydration products [30].The two bands are also related to the formation of secondary AFt,which be-come strong with the increased quantity of secondary AFt.In addition,the band at around 970cm −1comes from asymmetric stretching vibra-tion of Si –O in C –S –H gel [31,34].It can be observed from Fig.12that there is no obvious change in this band over the attack time,which sug-gests that the stability of C –S –H gel is independent of Na 2SO 4attack.With regard to FS,because chloride ions are not absorbed in the range 400–4000cm −1,the bands at around 730,530and 460cm −1,which are due to Al –O vibrations of [Al(OH)6]3−,can be identi ﬁed as the ﬁn-gerprint peaks of FS [35,36].Owing to the decomposition of FS under Na 2SO 4attack,the strength of these bands appears very weak.Fig.13shows the FT-IR spectra of samples CF and CG after the Na 2SO 4attack.There is no obvious band at around 3640cm −1in thespectra due to the consumption of CH induced by hydration reactions of FA and GGBS and sulfate attack.It can be observed from Fig.13that there is an increase in the strength of the band of C –S –H gel at 976cm −1in sample CF over the attack time from 56to 90days.Guerre-ro et al.attributed this to the further activating action on FA due to the increase in alkalinity induced by Na 2SO 4attack [15].Moreover,this re-sult also indicates that the stability of C –S –H gel is independent of Na 2SO 4attack.The difference of the bands at 714,535and 458cm −1be-tween samples CF and CG is slight.Fig.14shows the FT-IR spectra of samples CN and CM after Na 2SO 4and MgSO 4attack for 90days,respectively.It is observed from Fig.14that the strength of the band at around 710cm −1in sample CM is much stronger than that in sample CN.Also there is more FS in sample CM than in sample CN,which agrees with the results shown in Figs.10and 11.Moreover,it can be seen clearly from Fig.14that the strength of the band at around 970cm −1in sample CM is lower than that in sample CN.This is likely attributed to the decomposition of C –S –H gel induced by MgSO 4attack.As a result of that,the bound chlorides absorbed by C –S –H gel are released.A weak band at around 1110cm −1in sample CM due to the attack of MgSO 4can induce the formation of secondary AFt.4.3.Derivative thermo-gravimetric analysis (DTG)The DTG curves of sample CN attacked by Na 2SO 4are shown in Fig.15.There are some notable endothermic peaks in the DTG curves.The peak near 100°C is mainly attributed to the dehydration of C –S –H gel and AFt,which are dif ﬁcult to distinguish because of the overlap of dehydration temperature from 85to 130°C [23].The peak near 160°C is attributed to AFm [23].Besides these,the peaks near 340,450and 710°C are attributed to the dehydration of FS,CH and the decomposi-tion of calcite.The absence of the peak for FS in the DTG curve after the Na 2SO 4attack for 28days shown in Fig.15further demonstrates that the stability of FS is susceptible to Na 2SO 4attack.The change in the peak of AFm,which plays an important role in the formation of sec-ondary AFt during the Na 2SO 4attack,is also consistent with the change of FS.Fig.16shows the DTG curves of samples CF and CG after the Na 2SO 4attack for pared to sample CG,sample CF has a weak strength of the peak for FS,which is consistent with the analysis result shown in Fig.9and the R cl data shown in Fig.2.Fig.17shows similar DTG results of samples CN and CM after Na 2SO 4and MgSO 4attack for 90days.It is noticed from the ﬁgure that the strength of the peak for C –S –H gel and AFt in sample CM is far lower than that in sample CN.Ac-cording to the FT-IR results shown in Fig.14,this result further indicates that MgSO 4attack will lead to the decomposition of C –S –H gel,resulting in the release of bound chlorides.5.Discussion5.1.Stability of Friedel's saltSuryavanshi and Swamy reported that a drop in alkalinity of pore so-lution due to carbonation could induce the decomposition of FS [8].Con-versely,Na 2SO 4attack can increase the alkalinity of the pore solution,which has a negative effect on chloride binding [23,27,37].The question now is how Na 2SO 4attack affects the stability of FS.The exchange be-tween Cl −and SO 42−is the main mechanism in the formation of FS,which can be explained by the following reaction [27]:3CaO ·Al 2O 3·CaSO 4·12H 2O ðAFm Þþ2Cl −→3CaO ·Al 2O 3·CaCl 2·10H 2O ðFS ÞþSO 2−4þ2H 2O :ð14ÞEssentially,FS belongs to a phase of the AFm family,which has a complex chemical and structural constitution.A general formula for AFm phase is [Ca 2(Al,Fe)(OH)6]+X·m H 2O,where the bracketsindicateFig.7.Analysis of ettringite (AFt),Friedel's salt (FS)and calcium hydroxide (CH)in sample CN after Na 2SO 4attack for 0,28and 90days (wt.%represents the mass percentage of AFt/FS/CH in sample).217J.Geng et al./Cement and Concrete Research 68(2015)211–222。

EXECUTIVE SUMMARY..........................................................................

The ITS-IDEA program is jointly funded by the U.S. Department of Transportation’s Federal Highway Administration, National Highway Traffic Safety Administration, and Federal Railroad Administration. For information on the IDEA Program contact Dr. K. Thirumalai, IDEA Program Manager, Transportation Research Board, 2101 Constitution Avenue N.W., Washington, DC 20418 (phone 202-334-3568 fax 202-334-3471).IDEA PROJECT FINAL REPORTContract ITS-6IDEA ProgramTransportation Research BoardNational Research CouncilNovember 28, 1995LASER VEHICLEPrepared by:Richard Wangler Schwartz Electra-Optics, Inc.Orlando, FloridaINNOVATIONS DESERVING EXPLORATORY ANALYSIS (IDEA) PROGRAMS MANAGED BY THETRANSPORTATION RESEARCH BOARD (TRB)This investigation was completed as part of the ITS-IDEA Program, which is one of three IDEA programs managed by the Transportation Research Board (TRB) to foster innovations in surface transportation. It focuses on products and results for the development and deployment of intelligent transportation systems (ITS), in support of the U.S. Department of Transportation’s national ITS program plan. The other two IDEA programs areas are TRANSIT-IDEA, which focuses on products and results for transit practice in support of the Transit Cooperative Research Program (TCRP), and NCHRP-IDEA, which focuses on products and results for highway construction, operation, and maintenance in support of the National Cooperative Highway Research Program (NCHRP). The three IDEA program areas are integrated to achieve the development and testing of nontraditional and innovative concepts, methods, and technologies, including conversion technologies from the defense, aerospace, computer, and communication sectors that are new to highway, transit, intelligent, and intermodal surface transportation systems.The publication of this report does not necessarily indicate approval or endorsement of the findings, technical opinions, conclusions, or recommendations, either inferred or specifically expressed therein, by the National Academy of Sciences or the sponsors of the IDEA program from the United States Government or from the American Association of State Highway and Transportation Officials or its member states.TABLE OF CONTENTSEXECUTIVE SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1PROBLEM STATEMENT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 VEHICLE-SENSOR SURVEY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 PRODUCT DESIGN SPECIFICATION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4RESEARCH APPROACH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 RESULTS (8)CONCLUSION (9)GLOSSARY (10)REFERENCES (10)APPENDIX A: VEHICLE-SENSOR SURVEY (11)APPENDIX B:VEHICLE SPEED AND LENGTH MEASUREMENT ACCURACY (14)EXECUTIVE SUMMARYThis report describes a diode-laser-based vehicle detector and classifier (VDAC) developed by Schwartz Electro-Optics (SEO) under the Transportation Research Board (TRB) Intelligent Vehicle-Highway Systems (IVHS), now Intelligent Transportation Systems (ITS), Innovations Deserving Exploratory Analysis (IDEA) Program. The VDAC uses a scanning laser rangefinder to measure three-dimensional vehicle profiles that can be used for accurate vehicle classification. The narrow laser beam width permits the detection of closely spaced vehicles moving at high speed; even a 2-in.-wide tow bar can be detected. The VDAC shows great promise for applications involving electronic toll collection from vehicles at freeway speeds, where very high detection and classification accuracy is mandatory.The extensive network of modem highways in the United States today offers a fast, safe, convenient means of transporting goods and people within and between the major cities of the country. However, the U.S. highway system is under considerable stress. The traffic congestion that currently pervades metropolitan areas threatens future gridlock if mitigating steps are not soon taken. According to ITS America (I), “The percent of peak hour travel on urban interstates that occurred under congested conditions reached 70 percent in 1989, up from 41 percent in 1975 .”If this trend continues, all peak-hour traffic will be congested by 2000; there is good reason to believe that the trend will continue. FHWA data show that since about 1965 the number of vehicle miles traveled has been increasing at a faster rate than expenditures on highway maintenance and that total capital spending for highways, streets, roads, and bridges has declined by more than 50 percent. It is assumed that the growth in traffic and decline in new roadway construction will continue and that a worsening traffic congestion problem can be expected.One of the goals for ITS in the United States is to reduce congestion. Through areawide traffic management, ITS can use existing facilities to improve traffic-flow efficiency. Advanced sensor technology is needed to provide accurate, real-time traffic-parameter data, such as volume, occupancy, speed, and classification, which are required to optimize the performance of areawide traffic management systems. Information on real-time traffic conditions can be used for rapid incident detection and en-route driver navigation.The sensors of choice for many future ITS applications will undoubtedly be mounted overhead. Although inductive loops are simple, low-cost devices, they are not as easily installed or maintained because of their in-pavement location. Several types of overhead vehicle detectors are being developed (2), including video detection systems, microwave radar detectors, ultrasonic detectors, passive infrared sensors, and active infrared sensors. Of these, only the active infrared sensor, using a laser rangefmder, has the capability for accurate vehicle profiling as a result of the narrow angular beam width of the laser.This profiling capability, a dual-beam configuration that permits speed measurement, and efficient vehicle-recognition software combine to produce a sensor that can classify vehicles as well as measure their presence and speed. The outstanding utility of such a sensor became good motivation for its development as a practical device.VDAC relies on an inherent laser characteristic-narrow angular beam width--to provide the high resolution required for accurate vehicle, profiling. The VDAC beam-scan geometry is shown in Figure 1. The SCANNING BEAMSFIGURE 1 VDAC beam-scan geometry.1system scans two narrow laser beams, at a fixed angularseparation, across the width of a lane at a rate of up to 720scans/sec. Pulsed time-of-flight range measurementsprovide accurate _ (+ 3 in.) transverse height profiles of avehicle on each scan. The vehicle speed, determined fromthe time interval between the interceptions of the two laserbeams by the vehicle, is used to space the transverseprofiles appropriately to obtain the full three-dimensionalvehicle profile. An algorithm similar to those developedfor military target recognition is applied to the three-dimensional profile for vehicle-classification purposes.An example of the VDAC three-dimensional profilingcapability is provided by the range image shown in Figure2. This range image of a van pulling a boat traveling at aspeed of 45 mph was obtained by the VDAC operatingwith a scan rate of 360 scans/sec. The pixel spacingresulting from the l-degree scan resolution is more thanadequate for vehicle identification.VDAC uses a rotating polygon as shown in Figure 3 toline scan a diode-laser rangefmder across a 12-ft-widelane of highway. The polygon scanner rotatescontinuously in one direction at a constant speed. Theangle between each facet and the base of the polygonalternates between 87.5 and 92.5 degrees for adjacentfacets; as a result, successive scans are made with anangular separation of 10 degrees, which provides the twoseparate beams needed for speed measurements. Asshown in Figure 4, the 0.5- by 12-mrad laser beamilluminates a 5- by 120-mm spot on the pavement thatprovides good m-lane resolution and optimum cross-lanecoverage when the laser is pulsed once per degree of scanangle.Applications for VDAC are many and include thefollowing:l Vehicle classification for toll charging.l Use with wireless smart cards to prevent cheating byverifying vehicle classification.l Vehicle road location and timing determination forlicense plate photography.l Wide-area real-time surveillance for signalizedintersections and freeway monitoring.l Traffic parameter measurement such as average speed, road occupancy, traffic count by type of vehicle, and queue length at lights.l Very accurate vehicle presence detection.l Vehicle height measurement for bridge, tunnel, or overpass warning.l Road and freeway accident detection by traffic speed measurement.l Temporary emergency replacement for disabled in-pavement inductive loops.l Operation where inductive loops are impractical:bridges, parking garages, or cobblestone or brick streets.PROBLEM STATEMENT Because ITS is such a new program, a set of precise requirements for VDAC does not exist. The first several months of the project were used to establish these requirements through the aid of a vehicle sensor survey and phone conversations with potential users. After the survey results were analyzed, a detailed product design specification was generated.FIGURE 3 VDAC hardware showing rotating polygon.FIGURE 2 Three-dimensional range image of a van pulling a boat.23 6 9 12 15 18NUMBER OF VEHICLE CLASSESFIGURE 5 Example histogram showing number of vehicle classes required.The survey revealed that the most common VDAC requirements not satisfied by current sensors are vehicle separation and classification, particularly under high-volume, high-speed traffic conditions. Survey responses indicated interest in the following areas of application (in order of interest): (a) traffic data collection, (b) traffic signal control, (c) temporary installations, and (d) electronic toll collection. For the most part, it was not possible to categorize questionnaire response according to application area because respondents indicated an interest in more than one area. This was not true for the electronic toll collection area, however, which was of singular interest in three of four cases (e.g., Hughes Transportation Management Systems, Amtech Systems Corporation, and MFS Network Technologies). These potential VDAC users want sensors that are very accurate (99.9 to 99.9999 percent detection accuracy, 95 to 99.95 percent classification accuracy), highly reliable, and have a long lifetime (2.3 to 5 years). They are concerned about the effect of environmental conditions on sensor performance, particularly weather (rain, fog, snow) and temperature (minus 40o to 85o C). On the basis of their need for high detection and classification accuracy, the electronic toll collection companies appear to be prime customers for VDAC systems.4PRODUCT DESIGN SPECIFICATIONThe product design specification presented in Table 1 was established on the basis of (a) the results of a vehicle-sensor survey implemented via questionnaires mailed to potential VDAC users, (b) discussions with major ITS companies (e.g., MFS Network Technologies and Hughes Transportation Management Systems), and (c) previous SEO experience in developing diode-laser-based vehicle sensors.RESEARCH APPROACHA schematic diagram of the VDAC system is shown in Figure 6. The VDAC’s laser rangefmder uses an InGaAs diode-laser transmitter and a silicon avalanche photodiode (APD) receiver in a side-by-side configuration. The transmitter consists of the diode laser and its driver circuit and a collimating lens. The optical receiver is composed of an objective lens, narrow-band optical filter, detector-amplifier, and threshold detector.The laser diode used in the VDAC is an InGaAs injection laser diode having 12-W output at 10 A pulsed current drive. The laser driver produces a 10-A peak current pulse with a 3-nsec rise time and an 8-nsec pulseTABLE 1 VDAC SpecificationsSCAN RATEFIELD-OF-REGARDSCAN RESOLUTIONBEAM SEPARATIONRANGE MEASUREMENTS PER SCAN MAXIMUM RANGEMINIMUM RANGERANGE ACCURACYRANGE RESOLUTIONINTERFACELASER BEAM GEOMETRYLASER WAVELENGTHLASER EYE SAFETYPOWER SUPPLY VOLTAGE TEMPERATURE RANGEVEHICLE CLASSIFICATIONSPEED ACCURACY 360 SCANS / SEC / BEAM30”1”IO”3050 FT5 FT3 IN3 INRS422, RS232SOLID STATE RELAY- PRESENCE LOGIC-LEVEL (l-l-L) PRESENCEIN-LANE AXIS - 0.5 mradCROSS-LANE AXIS - 16 mrad904 nm“EYE SAFE”IN COMPLIANCE WlTH 21 CFR 1040 CDRH115VAC, 24VDAC-40o C TO 60o C11 CLASSESSPEED DEPENDENT (see Appendix B)width. A trigger pulse from the scanner control circuit triggers the laser at the proper scan angles. The 904-nm laser emission is at an ideal wavelength for the silicon APD receiver used.The optical detection circuitry converts optical radiation reflected from the vehicle and road to, first, an equivalent electrical analog of the input radiation and, finally, a logic-level signal. The logic-level signals are processed within the range counter logic to yield analog range data, which are read by the microprocessor.An analog range-measurement technique was chosen for VDAC because of its better resolution, smaller size, simpler circuitry, lower power consumption, and lower cost when compared with digital techniques. The analog range measurement circuit, know as a time-to-amplitude converter (TAC), has an accuracy of 1 percent of measured range and a resolution of plus or minus 3 in. TAC uses a constant-current source to charge a capacitor to obtain a linear voltage ramp whose instantaneous value is a measure of elapsed time. The circuit is designed so5that the voltage across the range measurement capacitor begins ramping down from the positive power supply when the laser fires. The ramp is stopped when either a reflected pulse is received or the end of the measurement period is reached. The TAC output is then converted to digital by a fast 1 O-bit analog-to-digital converter.The VDAC sofiware processes the range data and outputs vehicle classification, vehicle speed, and so forth, via a serial interface to a remote computer. The major software functions are identified in the block diagram shown in Figure 7. The algorithms that must be implemented for each function were developed and tested, to some extent, in previous projects. The vehicle detector and speed calculator are used in SEO’s Autosense I unit. The real-time range loop, calibration, and gain adjustment routines have been used in several other projects. The vehicle profiler and vehicle classifier are related to algorithms that have been designed and tested under military research programs. The VDAC rule-based classification algorithm will classify the 11 different types of vehicles shown in Figure 8.Speed, Etc. to PCSelf Tests,Calibration,Gain Adjustment,Threshold Adjust,Dew SenseFIGURE 7 Block diagram for major VDAC software functions.P CARMOTORCYCLE PICKUP TRUCK DELIVERY TRUCK BUSTRACTOR WITHOUT TRAILERTRACTOR WITH 1 TRAILERTRACTOR WITH 2 TRAILERSTRACTOR WITH 3 TRAILERSFIGURE 8 Eleven vehicle types classified by VDAC.Range data are used by the vehicle detection algorithmto determine when a vehicle is present. The vehicledetection algorithm first calculates the range to the roadand then sets a threshold above the road that is used todetermine the presence of a vehicle. A certain number ofconsecutive range samples above the detection thresholdare required to accurately detect the presence of a vehicleand reduce false alarms.RESULTSSE0 tested VDAC at a site in front of the SE0 facilitieson Florida SR 441. VDAC was mounted to a mast armextending over the curb lane of this major arterial asshown in Figure 9. Testing was carried out 24 hr/day foran extended period of time. This permitted testing undervaried traffic conditions, including peak-hour, off-peak,and stop and go, and under varied environmentalconditions such as rain, fog, and high temperature.During testing, the VDAC algorithm was modified asrequired to optimize vehicle detection and classificationcapabilities. The program code was uploadable to VDACvia the serial interface, making possible the real-timeoptimization of VDAC performance.FIGURE 9 VDAC mounted on mast arm.FIGURE 10 Computer display of real-time VDAC classification data.The vehicle profiles were collected and organized in adata base. By using the data base, specific vehicle typeswere extracted and used for vehicle-classificationalgorithm development. After the classification algorithmwas developed, a search of the data base provided datafrom similar vehicles for classification algorithm testing.The data base contains fields that include vehicle class,height, length, speed, and so forth, corresponding to eachvehicle detected. A video image was captured and storedfor each vehicle for easy verification of the vehicle-classification algorithm. A computer display of VDACclassification data, including vehicle profile and videoimage, is shown in Figure 10. Approximately 1,200vehicles per hour can be verified using the data basedisplay software. Currently 50,000 vehicles are logged inthe data base.vehicles. The top matrix shows the vehicle count and the bottom matrix the percentage of classification. The numbers along the diagonal of the bottom matrix show the percentage of classification for each vehicle class. Off-diagonal numbers show the possibility of confusion between specific vehicle classes. For example, 5.04percent of pickups were confused with passenger cars.The overall percentage of classification for all vehicle classes is shown in the lower right comer of Figure 11.CONCLUSION Tests performed have included detection accuracy,classification accuracy, and speed accuracy. Detection of100 percent was visually confirmed in a test of 10,000vehicles. The detection accuracy tests were performed infair weather with some light rain and therefore theaccuracy might degrade some during extended tests orduring severe weather conditions. Classification accuracyof 95.5 percent for 10 vehicle classes was achieved usingthe 50,000~vehicle data base. The confusion matrix(Figure 11) shows the classification results for the 50,000Schwartz Electra-Optics has developed a diode-laser-based vehicle detector-classifier that can accurately detect and classify vehicles moving at freeway speeds. Several major ITS companies have expressed a desire to purchase VDACs when they become available for electronic toll and traffic management (ETTM) applications. Such applications require sensors that are very accurate and highly reliable and have a long lifetime. SEO is confident that VDAC will prove useful for traffic surveillance and signal control as well as ETTM applications.VDAC may find its first implementation as part of the Toronto Highway 407 project for Hughes Traffic Management Systems, where 300 to 400 VDACs will be used as part of a completely automated overhead tollcollection system. In this ETTM application VDAC isrequired to provide accurate vehicle detection,classification, separation, lane position, and cameratrigger information to the roadside toll collection system.Production of VDACs for this project was to begin in thelast quarter of 1995.GLOSSARYSeparation-the ability to detect closely spaced vehicles Camera trigger-a signal generated by the VDAC when it detects the end of a vehicle. This signal can beused to trigger a video camera to capture an image ofthe vehicle’s license plate.as individual vehicles.Transverse height profile-the height profile measured across the vehicle from side to side.Classification-the capability of differentiating among types of vehicles.REFERENCESDetection-the ability to sense that a vehicle, whether moving or stopped, has appeared in the detector’s field of view.Detection response time-the time it takes to sense that a vehicle is in the detector’s field of view.1. Strategic Plan for intelligent Vehicle-Highway Systems,Report ITS-AMER-92-3. ITS America, Washington,D.C., 1992.2. Kell, J.H., I.J. Fullerton, and M.K. Mills. TrafficDetector Handbook, 2nd ed. Report FHWA-IP-90-002,U.S. Department of Transportation, July 1990.Electronic toll collection-the completely automated process of billing on toll roads using electronic communication with the ser-a device that amplifies light and produces an intense monochromatic beam.Scan resolution-the angle between successive range measurements.iscTrck/Bus/RV 0 0. .Tractor TrailerPickup 0.001 0.000.001 2.841FIGURE 11Vehicle classification confusion matrix.APPENDIX A:VEHICLE-SENSOR SURVEY Currently used sensor(s)TYPEREQUIREMENTS METREQUIREMENTS NOT METFUTURE REQUIREMENTSApplicationq Traffic signal controlq Traffic data collection[] Electronic toll collectionq Temporary Installations[]O t h e rCHARACTERISTICS DESIRED INVEHICLE DETECTOR/CLASSIFIER 1. Please rate the importance of these functional characteristics:LOW DETECT VEHICLE PRESENCE 1 2 3 MEASURE VEHICLE SPEED 1 2 3 MEASURE VEHICLE HEIGHT 1 2 3 MEASURE VEHICLE LENGTH 1 2 3 MEASURE VEHICLE WIDTH 1 2 3 VEHICLE CLASSIFICATION 1 2 3 SEPARATE CLOSE-SPACED VEH 1 2 3 DETECT TOW BARS 1 2 3 MULTIPLE LANE COVERAGE 1 2 3HIGH 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 76. Please specify required environmental conditions:AMBIENT TEMPERATURE RANGESHOCKVIBRATION7. Please circle the appropriate value for these general characteristics:PRICE 1 2 3 4 5 6 7 8 9 10 K$ SIZE 200 400 600 800 1000. 3m WEIGHT 2 4 6 8 10 12 14 16 18 20 lb POWER 1 2 3 4 5 6 7 8 9 10 W120 VAC 24VDAC 12VDAC OTHERAdditional Comments:。

百万智商测试题及答案

百万智商测试题及答案1. 问题：一个房间内有三盏灯，房间外有三个开关，每个开关对应一盏灯。

你只能进入房间一次，如何确定哪个开关控制哪盏灯？答案：首先，在房间外打开第一个开关，等待几分钟后关闭。

然后打开第二个开关，进入房间。

此时，亮着的灯是由第二个开关控制的。

如果是热的灯，则是由第一个开关控制的。

剩下的一盏灯由第三个开关控制。

2. 问题：一个数字序列是1, 2, 4, 7, 11, ...，这个序列的下一个数字是什么？答案：这个序列的规律是每一项都比前一项多1, 2, 3, 4, 5, ... 等递增的数。

所以下一个数字是11 + 5 = 16。

3. 问题：如果一个钟的时针和分针在12点整重合，下一次它们重合是几点？答案：下一次时针和分针重合将在12点05分多一点。

因为分针比时针快，所以它们每12小时重合一次，但不是正好在整点。

4. 问题：有5升和3升的水桶各一个，如何只用这两个水桶得到4升水？答案：首先用5升水桶装满水，然后倒入3升水桶直到满。

这样5升水桶里剩下2升水。

将3升水桶清空，把5升水桶中的2升水倒入。

再次用5升水桶装满水，然后倒入3升水桶直到满，这时5升水桶中就剩下4升水。

5. 问题：一个数字去掉最后一位是40，去掉第一位是13，这个数字是什么？答案：这个数字是143。

去掉最后一位是40，说明这个数字的后两位是40。

去掉第一位是13，说明这个数字的前两位是13。

6. 问题：一个农场有鸡和兔子共40只脚，如果鸡和兔子的数量相等，那么鸡和兔子各有多少只？答案：假设鸡和兔子各有x只。

鸡有2只脚，兔子有4只脚。

所以2x + 4x = 40，解得x = 5。

因此，鸡和兔子各有5只。

7. 问题：一个数加上100等于它自身乘以2，这个数是多少？答案：设这个数为x，根据题意，x + 100 = 2x。

解这个方程得x= 100。

8. 问题：有7克、2克砝码各一个，如何只用这两个砝码在天平上称出1克的重量？答案：首先用7克砝码和2克砝码在天平两边各放一个，使天平平衡。

第一百个客人答案

第一百个客人答案【篇一：顾客一百问及其答案】>1、手机三包都是哪几点啊？答：执行2001年11月15日实施的移动电话三包规定，具体的内容是：手机有性能故障无人为损害的前提下1、七天包退 2、15天包换、3一年内包修2、同样的机子，为什么你们这里的价格要贵些？答：我们是浙江省最大的手机销售企业，我们的手机都是从厂家直接进货的，在价格上有绝对优势，而且我们的报纸广告打的买贵退差价，能保证手机比别人便宜,除非他们那里活动，会有极个别特价机便宜点。

3、同样的手机在你们话机世界里面，价格都是相同的吗？答：有区域分别的，每个地区会有点不相同。

4、为什么你们都介绍我这款手机？答：这款手机是本店目前销售最好的，性价比很好，而且在送精美的礼品，所以顾客都喜欢。

5、你们这里买手机，对我们顾客有什么保障？答：我们的手机都是正规渠道进的货，绝对能保证产品的质量，经专业的检验，杜绝假冒伪劣。

无假货、水货、在同行业中率先提出了“假一罚十”的承诺，是浙江省诚信商业示范单位。

6、手机是怎么充电的啊？答：新手机前三次要带机充12小时，前三次最好用直充，以后再用座充。

直充相当于慢充，座充相当于快充。

7、一般手机待机有多长啊？答：现在的手机功能比较多，相对耗电比较大，说明书上写的待机时间都是在某种条件提供的实验室里，在没有插入sim卡的状态下进行的，与实际使用有所不同，具体使用时间视顾客使用情况及当地网络状况而定。

答：能上网。

但不是所有机型都能上网，要看gprs、wap功能有没有，同时sim卡要支持才行。

但最好不要在手机上经常下载东西，避免病毒。

9、手机为什么拨不出去电话？答：1、查看线路选择是否正常，是否选择了线路1、2、当地的网络信号较差，请转移到信号较强地区使用；3、当地的网络运营商忙线，可尝试稍后再拨；4、欠费10、我的手机是锂电池，一般晚上充电，可有时睡着了，一充就是一夜，不知是否有害？答：一般来说没什么问题，但是最好不要超过24小时，否则可能引起电池性能降低，甚至破坏。

14-6=8讲个故事

14-6=8讲个故事讲个故事，说一个傻子做梦他梦见他捡了100元钱，高兴地走回家时被路上一块大石头绊倒，醒来后发现真是捡到100元钱，并且又因为看到窗外天还没亮就从床上跳起来去马桶那儿小便，结果小便也把衣服弄湿了，回想着前面的事情，自言自语道：“我怎么不知道‘尿湿了’也算一件坏事呀？”。

再说另一个更傻的人。

他同样梦见自己捡到100元钱而高兴，却用自己所学习到的一点文化知识把捡到的100元钱数了6遍（这表示：怀疑、害怕和紧张），于是醒来后说：“今晚我的运气真好！我竟然碰巧遇到这么多好事！可惜我的钱却让我失望而归了！”当然我们都相信自己比别人聪明。

其实世界上根本就没有绝对聪明或者愚钝之分，能够区分出来这两类人最重要的标准在于他们所接受的教育程度。

而通常我们总会以一个人接触过的东西的广泛程度作为判断其社交水平的标志。

那么如何证明你聪明与否呢？要求你提供以下几条简单的推理题：1.把10只猴子分成两组，第一组每三只放在另一组中一只，共计五次，然后统计各组内猴子存活率。

2.某人养十二只羊，要吃七个月；有一只羊因为吃得太饱死掉了，另一只饿了三个月也被宰杀，然后拿剩余的八只羊和刚宰杀的羊作比较，问羊的平均寿命是多少？3.向别人借2000元买手机，但手机无法送达，第二年需偿还1600元，问该债务转移吗？4.在某超市购物卡中充值1000元，消费200元，取货100元，问该商店收入多少？5.若一位成功企业家与两名普通青年进行投资游戏，将成功企业家股票换成四个普通青年的股票，但两位普通青年已经赔光全部财产，求普通青年股票的赔率。

以上五个题目都难不住任何一个正常人。

什么叫笨呢？像第1题，你可以假设答案是百分之百确定的，即五只猴子中至少有两只是白痴，这样答案中便没有犯错误的空间了。

然而，通常情况下应该选择随机猜测。

如果它总是在2-7之间徘徊，则是白痴，反之则非。

记住：正确的答案永远只有一个！有些人认为世界是黑暗的，毫无希望的，除非一颗火星降临，将原本完美的宇宙烧毁，不然的话，永远不会有改变，永远沉浸在混乱之中。

网易有道面试测试题

网易有道面试测试题# 网易有道面试测试题一、逻辑推理题1. 一个房间里有三盏灯，房间外有三个开关，每个开关控制一盏灯。

现在你只能进入房间一次，如何确定哪个开关控制哪盏灯？2. 一个商人有一笔钱，他可以购买苹果或者橙子，苹果每斤5元，橙子每斤3元。

如果商人用这笔钱购买尽可能多的水果，他应该选择哪种水果？二、技术能力测试1. 描述一下你对RESTful API的理解，并给出一个例子。

2. 请解释什么是数据库的事务，并说明其ACID属性。

三、编程题1. 给定一个整数数组，找出其中的最大值和最小值，并返回它们的索引。

2. 实现一个函数，检查一个字符串是否是回文，忽略空格、标点和大小写。

四、产品设计题1. 如果让你设计一个在线词典应用，你会考虑哪些功能？2. 描述一个你认为可以提升用户学习效率的功能，并解释其工作原理。

五、案例分析题1. 假设你是网易有道词典的产品经理，面对用户反馈的翻译不准确问题，你会如何分析并解决？2. 描述一个你认为成功的产品案例，并分析其成功的原因。

六、英语能力测试1. 翻译以下句子：“The early bird catches the worm.”2. 阅读以下段落，并总结其主要观点（英文回答）："In recent years, the trend of remote work has been on the rise. Companies have realized the benefits of allowing employees to work from home, such as reduced overhead costs and increased employee satisfaction. However, this shift has also brought about new challenges, such as maintaining team cohesion and ensuring productivity."七、开放性问题1. 你认为在线教育行业面临的最大挑战是什么？2. 如果你有机会与业界领袖进行对话，你会问他们什么问题？请注意，这些题目只是示例，实际面试中可能会根据具体职位和公司需求有所不同。

攻克大厂笔试题及答案

攻克大厂笔试题及答案1. 编程题：字符串反转- 题目描述：给定一个字符串，请编写一个函数，实现字符串的反转。

- 输入：字符串 `s`- 输出：反转后的字符串- 示例：- 输入：`hello`- 输出：`olleh`- 答案：```pythondef reverse_string(s):return s[::-1]```2. 算法题：寻找缺失的数字- 题目描述：给定一个包含 `n` 个元素的数组，其中 `n` 个连续整数从 `1` 到 `n`，但有一个数字缺失。

请找出缺失的数字。

- 输入：数组 `nums`- 输出：缺失的数字- 示例：- 输入：`[3, 2, 1]`- 输出：`4`- 答案：```pythondef missing_number(nums):expected_sum = len(nums) * (len(nums) + 1) // 2actual_sum = sum(nums)return expected_sum - actual_sum```3. 数据结构题：链表反转- 题目描述：给定一个单链表的头节点，请实现一个函数，将链表进行反转，并返回反转后的头节点。

- 输入：链表头节点 `head`- 输出：反转后的链表头节点- 答案：```pythonclass ListNode:def __init__(self, val=0, next=None):self.val = valself.next = nextdef reverse_list(head):prev = Nonecurrent = headwhile current:next_node = current.nextcurrent.next = prevprev = currentcurrent = next_nodereturn prev```4. 系统设计题：设计一个缓存系统- 题目描述：设计一个缓存系统，要求支持以下操作：- `get(key)`: 如果键存在于缓存中，则获取其数据值（总是正数），否则返回 -1。

100个囚犯和灯泡的那些事儿[技巧]

100个囚犯和灯泡的那些事儿说有 100 个囚犯分别关在 100 间牢房里。

牢房外有一个空荡荡的房间，房间里有一个由开关控制的灯泡。

初始时，灯是关着的。

看守每次随便选择一名囚犯进入房间，但保证每个囚犯都会被选中无穷多次。

如果在某一时刻，有囚犯成功断定出所有人都进过这个房间了，所有囚犯都能释放。

游戏开始前，所有囚犯可以聚在一起商量对策，但在此之后它们唯一可用来交流的工具就只有那个灯泡。

他们应该设计一个怎样的协议呢？这个经典的问题在网上转载无数，题目描述被好事者们改得天花乱坠，甚至加进了“这盏灯永远有充足的能源供应”、“如果灯泡坏了或是电路出了故障会马上修好”等条件，剥掉了“算法问题”的外壳，填补了本不存在的漏洞，让更多的人动起了脑筋。

在论坛上，每次贴出这个问题，总会引起一大群人的口水战。

但很不幸的是，这个题目的来源至今仍是个谜。

据目前的已知情况推测，这个题目最早来源于 Berkeley 的电气工程荣誉学会，时间大概是 2001 年。

在 2002 年的 7 月， IBM 的 Ponder This 趣题栏目介绍这个题目，囚犯与灯泡一炮走红，随即遍布网络的各个角落。

2003 年， The Mathematical Intelligencer 杂志上发表了一篇题为 One hundred prisoners and a lightbulb 的论文，也让囚犯们正式引起了数学家们的关注。

相信这个问题的答案大家已经非常熟悉了，不过这里我想用另一种更玄乎的、更具启发性的方式重新讲述一下答案。

不妨幻想房间中有一个盒子，盒子里可以容纳一个小球。

灯泡亮就表示这个假想的盒子里有一个假想的小球，灯泡不亮就表示这个假想的盒子是空的。

因此，用开关控制灯泡就相当于在盒子里放进小球或者取走小球。

初始时，每个囚犯手中都有一个小球（当然这个小球也是囚犯们自己意淫出来的）。

游戏开始前，囚犯们选择一个代表作为统计者。

之后，每次有囚犯进入房间后，如果小球还在他手里，盒子恰恰又是空着的，他就把小球放进去；而统计者的任务就是收集小球——每次进入房间后，看到盒子里有小球就把它拿走。

谷歌15个让人疯狂的经典问题

谷歌15个让人疯狂的经典问题谷歌15个让人疯狂的经典问题你能回答几个对一些身处经济衰退大潮中的初级经理和软件开发者而言，谷歌是一个避风港。

但其招聘门槛较高，首先，谷歌更青睐长春藤联盟(由美国八所知名大学所组成)的毕业生；其次，即使应聘者已年过30，谷歌也很在意其GPA(平均成绩点数)分数；第三，谷歌需要的是那些想改变世界的人。

而且，即使应聘者满足了上述要求，也有可能在面试中被谷歌提出的问题所难倒。

以下是15个让许多应聘者抓狂的谷歌面试题。

问题1：一辆校车能装下多少个高尔夫球？应聘职位：产品经理问题2：如果让你清洗西雅图市所有的窗户，你会对此索价多少？应聘职位：产品经理问题3：在一个重男轻女的国家里，每家每户都想生男孩。

若一户人家生了一个女孩，便会再生一个，直到生下的是男孩为止。

请问这个国家的男女比例是多少？应聘职位：产品经理问题4：全世界共有多少位钢琴调音师？应聘职位：产品经理问题5：下水道井盖为什么是圆的？应聘职位：软件工程师问题6：为旧金山市设计一个紧急疏散方案。

应聘职位：产品经理问题7：时钟的指针一天内总共会重合多少次？应聘职位：产品经理问题8：阐释“死牛肉”的意义所在。

应聘职位：软件工程师问题9：一个人开车来到旅馆，变得一无所有。

究竟发生了什么事情？应聘职位：软件工程师问题10：你想知道好友鲍勃是否有你正确的电话号码，但又不能直接问他。

你必须在卡片上留言，让伊芙将卡片较交给鲍勃。

除了问题以外，你还应该在卡片上写什么，才能既确保鲍勃能看懂留言，又使伊芙看不出卡片上写有你的电话号码。

应聘职位：软件工程师问题11：你是一艘海盗船的船长，你的船员要投票决定如何平分金条。

如果与你意见一致的船员数量少于一半，你将被杀死。

你应该如何提议分配金条，才能既分得较多赃物，又能活下来？应聘职位：工程经理问题12：你有8个大小一样的球，其中7个重量相同，只有一个略重一些。

给你一个天平，而且只准称两次，如何找出重量不同的那个球？应聘职位：产品经理问题13：你在一幢100层高的大楼中，给了你两个鸡蛋。

人际逻辑经典题

人际逻辑经典题
以下是一道人际逻辑经典题:
题目:在一条船上，有100个人。

每个人有一个箱子。

这些箱子里有金子和宝石，每个人拥有的金子和宝石数虽都不同。

每个人对自己的箱子里的东西都非常了解，但不知道其他人的箱子里有什么。

有一天，船长发现有人偷偷拿了一些金子和宝石。

为了找出这个人。

船长想了一个办法:他让所有的人把自己的箱子都打开，并让每个人都把自己的金子和宝石数量写在一张纸上。

然后，船长把所有的纸放在一起，随机抽了一张纸，说这张纸上写的东西是假的。

现在。

根据这个信息。

你要判断出谁是小偷。

答案解析:假设每个人写的都是真的，那么拿到假纸条的人就是小偷。

因为小偷不知道其他人箱子里有什么，所以他写的是假的。

而其他人写的都是真的。

所以他们看到假纸条后会知道自己不是小偷。

所以拿到假纸条的人就是小偷。

这道题考察的是人际逻辑推理能力，通过给出的信息来判断出谁是小偷。

2021年名企考试题IT公司的面试题

名企考试题IT公司的面试题名企考试题汇总IT公司的面试题网络 ___:IT公司的题1.指出以下服务所默认的端。

(6分)FTP： Tel： POP3： ___TP：PCAnyWhere： Windows终端服务：微软用来测试应聘者的试题。

它主要考察受训者的逻辑思维和判断能力，同时也给受训者一些关于问题解决方法上的启示。

游戏规则和程序1.有两个 ___，一间房里有三盏灯，另一间房有控制着三盏灯的三个开关，这两个 ___是分割开的，从一间里不能看到另一间的情况。

2.现在要求受训者分别进这两 ___一次，然后判断出这三盏灯分别是由哪个开关控制的。

3.有什么办法呢？相关讨论1.请受训者说出解决这个问题的关键在哪里？2.有没有想过电能够发热的特性？总结在工作中经常会有一些难题需要用平时积累的生活知识来解决，这个游戏就是很好的提示。

答案1.先走进有开关的 ___，将三个开关编号为a b c。

2.将开关a 打开5分钟，然后关闭，然后打开b3.然后走到另一个 ___，即可辨别出正亮着的灯是由b 开关控制的.。

再用手摸另两个灯泡，发热的是由开关a 控制的，另一个就一定是开关c了。

?形式：个人完成时间：3分钟材料：无场地：不限应用：(1)创造性思维的产生?(2)打破传统思维的局限?三个灯泡有两间屋，甲和乙，甲屋有三个开关，乙屋有三个灯泡，甲屋是看不到乙屋，而甲屋的每一个开关是控制乙屋的其中一个灯泡，问你怎样可以只停留在甲屋一次，停留在乙屋一次，而可以知道哪个开关是控制哪个灯泡呢？答案：先去甲屋开一个开关，等一会，然后关掉它，再开另一个开关，再走到乙屋，热而不亮的一个灯泡是第一个开关所控制，亮的便是第二个，不亮又不热的便是第三个开关所控制了。

模板,内容仅供参考。

名企面试试题——Google

名企面试试题——Google（最新版）编制人：__________________审核人：__________________审批人：__________________编制单位：__________________编制时间：____年____月____日序言下载提示：该文档是本编精心编制而成的，希望大家下载后，能够帮助大家解决实际问题。

文档下载后可定制修改，请根据实际需要进行调整和使用，谢谢!Download tips: This document is carefully compiled by this editor.I hope that after you download it, it can help you solve practical problems. The document can be customized and modified after downloading, please adjust and use it according to actual needs, thank you!正文内容这次是连环游戏，每一题的答案将在下一题中用到。

1、{first 10-digit prime found in consecutive digits e}.com. e中出现的连续的第一个10个数字组成的质数。

2、 Congratulations,Youve made it to level 2. Go to /labjobs/ via: Google recruits eggheads with mystery billboard Mysterious Billboard May Be Google Recruitment Ad Myserious billboard Googleis behind mystery geek trap 写一句俳句来描述搜索流量季节性预测的可能方法。

世界500强企业10秒钟淘汰求职者最爱的12个推理题共9页word资料

世界500强企业10秒钟淘汰求职者最爱的12个推理题世界500强企业之所以强，是因为他们有强大的人力资源，这很大功劳都归功于他们的HR，为何他们的HR能够招聘到优秀的人才呢？下面就是世界500强淘汰求职者常用的12道推理题。

1、水平思考法有一家人决定搬进城里，于是去找房子。

全家三口，夫妻两个和一个5岁的孩子。

他们跑了一天，直到傍晚，才好不容易看到一张公寓出租的广告。

他们赶紧跑去，房子出乎意料的好。

于是，就前去敲门询问。

这时，温和的房东出来，对这三位客人从上到下地打量了一番。

丈夫豉起勇气问道：“这房屋出租吗？”房东遗憾地说：“啊，实在对不起，我们公寓不招有孩子的住户。

”丈夫和妻子听了，一时不知如何是好，于是，他们默默地走开了。

那5岁的孩子，把事情的经过从头至尾都看在眼里。

那可爱的心灵在想：真的就没办法了？他那红叶般的小手，又去敲房东的大门。

这时，丈夫和妻子已走出5米来远，都回头望着。

门开了，房东又出来了。

这孩子精神抖擞地说：……房东听了之后，高声笑了起来，决定把房子租给他们住。

问：这位5岁的小孩子说了什么话，终于说服了房东？2、篮球赛在某次篮球比赛中，A组的甲队与乙队正在进行一场关键性比赛。

对甲队来说，需要嬴乙队6分，才能在小组出线。

现在离终场只有6秒钟了，但甲队只蠃了2分。

要想在6秒钟内再赢乙队4分，显然是不可能的了。

这时，如果你是教练，你肯定不会甘心认输，如果允许你有一次叫停机会，你将给场上的队员出个什么主意，才有可能蠃乙队6分？3、分油问题有24斤油，今只有盛5斤、11斤和13斤的容器各一个，如何才能将油分成三等份？[page]4、第十三号大街史密斯住在第十三号大街，这条大街上的房子的编号是从13号到1300号。

琼斯想知道史密斯所住的房子的号码。

琼斯问道：它小于500吗？史密斯作了答复，但他讲了谎话。

琼斯问道：它是个平方数吗？史密斯作了答复，但没有说真话。

琼斯问道：它是个立方数吗？史密斯回答了并讲了真话。

乐考推理题

乐考推理题
乐考推理题有一天，美国一家著名的电脑公司召开记者招待会。

出席会议的除该公司的董事长外，还有该公司的总经理和技术员工代表。

那天恰好只有这三位与会者没去参加，所以记者不得不采访他们当中的每一位。

在回答问题之前，董事长说:我希望大家能够解释我们今晚不来的原因，并且说明如果由此给公司造成损失，将承担怎样的责任。

然后又请总经理说明其意见。

最后，记者询问技术员工代表。

员工代表则显得非常镇定地回答道：“因为那两位董事和所有的董事会成员，都同时收到了该公司董事长的信件。

”那么根据上述情况，请你对以下各项作出判断。

“你认为是什么？”(判断对错) A.总经理和技术员工代表可能同时被陷害而被炒鱿鱼 B.那两位董事与所有董事均收到了董事长的邀请 C.信函是技术员工发送的 D.那两位董事已遭到调查先看第一个答案：公司的所有人都在下班前走了，也就是说董事长无法知晓这封邀请函的内容，所以技术员工无罪。

接着分析第二个。

总经理虽然也收到了董事长的信函，但信函中却写明不许向外传播，所以总经理犯规。

这次游戏的结局是美国电脑公司将其关闭了事。

，再来看看第三个。

信函是从技术员工手中丢出的，也就是说从技术员工自己的口袋里掏出来的，证明信函并不是直接寄往外界的，所以技术员工也不构成违规行为。

故排除第四、五两个选项。

最终的判断结果是技术员工犯规。

“你认为是什么？
- 1 -。

悦刻面试逻辑思维题及答案

悦刻面试逻辑思维题及答案
1.有个小镇有100对夫妇，每个丈夫都在欺骗他的妻子。

妻子们都无法识破自己丈夫的谎言,但是她们却能知道其他任何一个男人是否在撒谎。

镇上的法律规定不准通奸，好-旦证明丈夫不忠就应该立刻杀死他，镇上所有妇女都必须严格遵守这项法律。

有一天,镇上的女王宣布，至到有一个丈夫不忠的。

结果小镇前99天无事儿，而在第100天发生了答屠杀。

这是怎么发生的呢?
答:这就是黑帽和白帽的题。

前99天无事儿，说明每个妻子都知道除了自己丈夫外的另外99个男人都通奸，因此,也就确定了自己的男人也通奸。

2.有5个海盗,按照等级从5到1排列。

最大的海盗有权提议他们如何分享100枚金币。

但其他人要对此表决，如果多数反对,那他就会被杀死。

他应该提出怎样的方案，既让自己拿到尽可能多的又不会被杀死?
答:98 1010
析:倒推。

1)如果只剩两个人，除非全给最后-个人，否则最后一个人肯定反对，因此最后一人不管怎样总要反对;2)如果剩3人，只要给第四人1枚金币，他就可以赢得半数以上同意,因此第三人肯定反对;3)如果剩4人，于第三人和第五人肯定反对，他除非不拿金币，否则肯定得不到半数以上的支持;4)因此, 5人时，第一人只要获得第二人和第四人的支持即可。

100囚犯问题的初步探究

100囚犯问题的初步探究2020年12月8日支太坤、问题：有100个无期徒刑囚徒，被关在100个独立的小房间，互相无法通信。

每天会有一个囚徒被随机地抽出来放风，随机就是说可能被抽到多次。

放风的地方有一盏灯，囚徒可以打开或者关上，除囚徒外，没有别人会去动这个灯。

一天，全体囚徒大会，国王大赦，给大家一个机会：从明天开始，如果某一天，某个囚徒能够明确表示，所有的囚徒都已经被放过风了，而且的确如此，那么所有囚徒释放；如果仍有囚徒未被放过风，那么所有的囚徒一起处死！各位囚犯只有在这场大会其中20分钟的时间可以交流，之后无法进行任何交流。

请问你如何让这100个囚犯能顺利释放。

补充说明：这盏灯会永远有充足的能源供应，灯泡和电路不会出故障。

除了开关这盏灯，放风的囚犯放风时留下的任何其它痕迹都会在夜晚被清除干净（包括在灯上作的任何记号）。

牢房是完全封闭的，院子里的灯光在牢房里看不到。

只有放风到院子里的人才能看到。

1.1策略解析问题的实质其实是：用1bit的储存空间更可能多的存储信息。

显然，如果没有任何策略，只靠自己的猜测与运气，这100个囚犯释放的概率无限接近0，因此我们需要一个策略，来保证，至少是增大囚犯释放的概率。

仔细研究问题，我们发现了以下几个关键点。

1、囚犯的放风是随机的，可能有的是连续被抽多次，有的可能很长时间才放风2、囚犯唯一能知晓并控制的因素为灯的开关1.2 固定领袖策略基于上文分析的关键点，我们尝试先找出一个人作为领袖，称之为leader。

只有领袖才能关闭灯，其余所有人只能开灯。

很显然，领袖的产生对本策略十分重要，在此，我们先尝试固定领袖，即在策略开始前，固定选出一人领袖。

开始放风的第一天：除领袖外，不管谁去放风，都把灯灭了。

在这之后出去放风的囚犯，只要看到灯是灭的，那么不要对灯做任何操作（如果第一天领袖就出去放风，那么领袖此时把灯打开并记下开灯次数），直到某一天，轮到领袖去放风。

领袖放风的时候，看到灯是灭的，那么就把灯点亮，并记下电量灯的次数，。