24点游戏结果大全

24点游戏

最绝的是：(0!+0!+0!+0!)!=24 ,0!是0的阶乘，值为1。

先考虑只用1--9,共9个数字的情况：

4个都不一样ABCD： C（4，9）=9*8*7*6/（4*3*2*1）=126；

4个都一样AAAA： C（1，9）=9；

4个中有三个一样ABBB：P（2，9）=9*8=72

4个中有两对AABB： C（2，9）=9*8/2=36

4个中有一对AABC： C（3，9）*3=9*8*7/2=252

所以共有：C(4,12)=126+9+72+36+252=495 404:91:(56)

注：另解可用开平方√及次方，考虑另解的话，仅有35个无解（7%）

一。4个都一样AAAA：C（1，9）=9 4:5

无解的有：1111，2222，7777，8888，9999

另解(2)：8888：8+8+√8*8 9999Æ3333

3333: 3X3X3-3 4444: 4X4+4+4 5555: 5X5-5/5 6666: 6+6+6+6

若考虑阶乘,1111 : (1+1+1+1)! 2222: (2+2+2-2)!

二。4个中有两对AABB： C（2，9）=9*8/2=36 24:12

无解的有: 1122,1133,1177,4466,6677,7788

99AA除9955,9933外都无解.(9911,9922,9944,9966,9977,9988)

另解(8):9911Æ3911 99AAÆ33AA 4466Æ2266 7788: 8x√(8+7/7)

若考虑阶乘, 1122: (1-1+2+2)! 1133: (3+3-1-1)!

AA55: 5X5-A/A

1144: (1+1+4)X4 1166: (6-1-1)X6 1188:(1+1)x8+8 2233: (3+3)X2X2

2244:(2x4-2)x4 2266: (6+2)X6/2 2277:2x(7+7-2) 2288: 2X2X8-8

3344: 4x3+4X3 3366:3X(6/3+6) 3377:(3/7+3)x7 3388:8/(3-8/3)

3399: 3X9-9/3 4477:(4-4/7)X7 4488: 4+4+8+8 6688:6x8/(8-6)

三。4个中有三个一样ABBB：P（2，9）=9*8=72 43:29

无解的有: 1222,2555,3555,6222,7555,7666,7888,8555,9888

111A除1118外都无解.(1112,1113,1114,1115,1116,1117,1119)

777A除7773,7774外都无解.(7771,7772,7775,7776,7778,7779)

999A除9993外都无解.(9991,9992,9994,9995,9996,9997,9998)

另解(12)：1115: 5１＋１-1 2555：5２–5/5 6222:6X2X√(2X2) 9888Æ3888

7779Æ7773 999AÆ333A

若考虑阶乘,1222: (1+2+2/2)! 3555:(3+√(5X5)/5)!

1112: (1X1+1+2)! 1113:(1X1X1+3)! 1114: (1-1+1X4)!

1116:(-1-1+1X6)! 1117: (-1-1-1+7)! 1119: (1+1-1+√9)!

7772: (7-7/7-2)! 7775: (5-√(7X7)/7)!

AAA(24-3A):A+A+A+(24-3A) AAA(3A-24):A+A+A-(3A-24)

设AB=24，有：ABBB：AXBXB/B (A+1)BBB:(A+1-B/B)XB (A-1)BBB:(A-1+B/B)XB

A(B+1)(B+1)(B+1):AX(B+1-(B+1)/(B+1)) A(B-1)(B-1)(B-1):AX(B-1+(B-1)/(B-1)) 333A,444A都有解。666A除6667外都有解。

1333:(1+3)X(3+3) 1444:(4+4)X(4-1) 1555:(5-1/5)x5 1666:(6-1)x6-6 1888:(8+8+8)X1

2333:(3X3+3)X2 2444:4X4+4X2 2666:2X6+6+6 3222:3X2X2X2 3444:(3+4)x4-4

4222:4X(2+2+2) 4333:4X(3X3-3) 5222:(5x2+2)x2 5333:5x3+3x3 5888:5X8-8-8 6888:(8-6)x8+8 7222:(7x2-2)x2 8111:8x(1+1+1) 8666:(6+6-8)X6 9222:(9+2)x2+2 9444:(9-4)X4+4 9666:(9-6)X6+6

四。4个都不一样ABCD： C（4，9）=9*8*7*6/（4*3*2*1）=126 124:2

无解的有:1678,3467

另解(1):3467Æ3267

若考虑阶乘,1678: (6-1-8+7)!

1234:1X2x3x4 1235:(1+2+5)x3 1236:(2+3-1)X6 1237:1+2+3X7 1238:8X3/(2-1)

1239:(9+3)X2X1 1245:4X(2+5-1) 1246:6X4/(2-1) 1247:(7+2-1)X4 1248:(4+8)x2x1

1249:4X(9-1-2) 1256:(5+1-2)X6 1257:(7+1)X(5-2)1258:8X(5-2)X1 1259:2X9+1+5

1267:6X(7-1-2) 1268:8X6/2X1 1269:(9-1)X6/2 1278:2X8+1+7 1279:2X9+7-1

1289:2X8+9-1 1345:4X5+3+1 1346:6/(1-3/4) 1347:4X7-3-1 1348:4X(8+1-3)

1349:(9-3)X4X1 1356:3X6+1+5 1357:(7-3)X(5+1)1358:3X5+1+8 1359:(9-3)X(5-1) 1367:3X6+7-1 1368:(6-3)X8X1 1369:(9/3+1)X6 1378:8X(7-3-1) 1379:(1+7)X9/3 1389:9/3X8X1 1456:4/(1-5/6) 1457:4X7-5+1 1458:(5-1)X4+8 1459:5X(4-1)+9 1467:6X(7-4+1) 1468:(6+1-4)X8 1469:(9-4-1)X6 1478:(7-4)x8X1 1479:(9-1)X(7-4) 1489:4X8-9+1 1567:5X6-7+1 1568:(8-5+1)X6 1569:(9-5)X6X1 1578:(7-5+1)X8

1579:(7-1)X(9-5)1589:(9-1-5)X8 1679:(7+1)X(9-6)1689:1+6+8+9 1789:7+8+9X1

2345:2X(3+4+5) 2346:6X4X(3-2) 2347:(7-3)X(2+4)2348:8X(2+4-3) 2349:(9+3)X4/2 2356:6X(5+2-3) 2357:3X5+2+7 2358:2X8+3+5 2359:3X9+2-5 2367:3X7+6/2

2368:3X6+8-2 2369:(9-2-3)X6 2378: (7-3)X(8-2)2379:2X(3X7-9) 2389:(9-3)X8/2 2456:(4+5)X2+6 2457:(7+5)x4/2 2458:(2+5-4)X8 2459:(5+9)X2-4 2467:2X7+4+6 2468:(8/4+2)X4 2469:(9-6)X2X4 2478:4X7-8/2 2479:7+9+2X4 2489:8X(9-2-4)

2567:2X6+5+7 2568:2X5+6+8 2569:6/2X5+9 2578:8X(2X5-7) 2579: 5X7-2-9 2589:(9-5)X(8-2)2678:(7+2-6)X8 2679:(9+2-7)X6 2689:2/6X8X9 2789:2X(7+9)-8

3456:(3+5-4)X6 3457:4X5+7-3 3458:3X8X(5-4) 3459:3X(9+4-5) 3468:3X4X(8-6) 3469:(9+3)X(6-4)3478:(7-3)X4+8 3479:3X9-7+4 3489:(3+9)X8/4 3567:(5+7)X6/3 3568:8X3X(6-5) 3569:(3+5)X(9-6) 3578:3X7+8-5 3579: 3+5+7+9 3589:(8-5)X9-3 3678:3+6+7+8 3679:3X7+9-6 3689:(6-9/3)X8 3789:3X(7+9-8) 4567:(7+5)X(6-4) 4568:(4+5-6)X8 4569:4+5+6+9 4578:4+5+7+8 4579:4X9-5-7 4589:4X(5+9-8) 4678:4X6X(8-7) 4679:(7+9)/4X6 4689:4X6X(9-8) 4789:4X(7+8-9) 5678:(5+7)X(8-6) 5679:(7-5)X9+6 5689:(5+8-9)X6 5789:(5+7-9)X8 6789:8X6/(9-7)

五。4个中有一对AABC： C（1，9）*C（2，8）=9*8*7/2=252 209:43

无解的有：

1123,1124,1125,1159,1167,1178,1179,1189,2213,2279,3324,3358,4459,4467,5513, 5517,5518,5526,5569,5579,6617,6678,7715,7716,7718,7726,7729,7735,7749,7758,

7768,7769,7789,8834,8867,9912,9914,9918,9925,9927,9957,9958,9978

22AB，33AB，44AB，66AB，88AB都仅各有两个无解。

11AB，55AB，77AB，99AB分别各有8，6，11，8个无解。

另解有(33)：1125：5２–1X1 1159Æ1153 1178:8x√(7+1+1) 1179Æ1173 1189Æ1183