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[分享][趣题征解] 2010 最小问题

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发表于 2010-4-29 23:43 | 显示全部楼层 |阅读模式
[这个贴子最后由elimqiu在 2010/04/30 10:15pm 第 1 次编辑]

设 a,b,c 是正整数且 a+b+c = 2010
在所有可能的a,b,c得取法中,求最小 m 使得 a!b!c! = (10^m)G 其中整数 G 不能被10整除。
发表于 2010-4-30 11:30 | 显示全部楼层

[分享][趣题征解] 2010 最小问题

[这个贴子最后由luyuanhong在 2010/04/30 11:32am 第 1 次编辑]

一个数的阶乘 n!中,含有的因子 10 的幂次数,可以这样来计算:
n!中因子 10 的幂次数=[n/5]+[n/25]+[n/125]+[n/625]+ … 。
把 2010 拆成 a+b+c ,要想使 a!b!c!中因子 10 的幂次数尽可能低,就要使得
a、b 都正好比 5、25、125、625 的倍数少一点,使得它们除以 5、25、125、625 后,
作取整运算时,可以得到小一点的整数。c 也不要正好等于 5、25、125、625 的倍数。
所以,可以取 a=b=624 ,c=762 。这时,
a!、b! 中因子 10 的幂次数 =[624/5]+[624/25]+[624/125]+[624/625]
   =[124.8]+[24.96]+[4.992]+[0.9984]=124+24+4+0=152 ;
c! 中因子 10 的幂次数 =[762/5]+[762/25]+[762/125]+[762/625]
   =[152.4]+[30.48]+[6.096]+[1.2192]=152+30+6+1=189 。
这时,a!b!c!中因子 10 的幂次数 m =152+152+189=493 。
 楼主| 发表于 2010-4-30 21:30 | 显示全部楼层

[分享][趣题征解] 2010 最小问题

这样的分析很直观
 楼主| 发表于 2010-5-1 00:14 | 显示全部楼层

[分享][趣题征解] 2010 最小问题

  1. def cc(n):
  2.     s=0
  3.     d=5
  4.     c=n/5
  5.     while c> 0:
  6.         s+=c
  7.         d*=5
  8.         c=n/d
  9.     return s
  10. def mm():
  11.      mm=3*cc(670)
  12.      ll=[670,670,670]
  13.      for a in range(1,671):
  14.          for b in range(a,(2010-a)/2+1):
  15.              c=2010-a-b
  16.              d=cc(a)+cc(b)+cc(c)
  17.              if mm>d:
  18.                  mm=d
  19.                  ll[0]=a
  20.                  ll[1]=b
  21.                  ll[2]=c
  22.      return mm,ll
  23. mm()
  24. (493, [137, 624, 1249])
复制代码
可见 a = 137, b = 624, c = 1249 也达到最小m值
 楼主| 发表于 2010-5-1 04:11 | 显示全部楼层

[分享][趣题征解] 2010 最小问题

[这个贴子最后由elimqiu在 2010/04/30 09:13pm 第 1 次编辑]

当a,b,c 为整数且 1 ≤ a ≤ b ≤ c,a + b + c = 1 时, 有2712种方法使得 a!b!c! 的10-因子
个数最小。 其中 【624, 624, 762】 使得 a!b!c! 在这些解中最大
[137, 624, 1249], [138, 623, 1249], [138, 624, 1248], [139, 622, 1249], [139, 623, 1248],
[139, 624, 1247], [142, 619, 1249], [142, 624, 1244], [143, 618, 1249], [143, 619, 1248],
[143, 623, 1244], [143, 624, 1243], [144, 617, 1249], [144, 618, 1248], [144, 619, 1247],
[144, 622, 1244], [144, 623, 1243], [144, 624, 1242], [147, 614, 1249], [147, 619, 1244],
[147, 624, 1239], [148, 613, 1249], [148, 614, 1248], [148, 618, 1244], [148, 619, 1243],
[148, 623, 1239], [148, 624, 1238], [149, 612, 1249], [149, 613, 1248], [149, 614, 1247],
[149, 617, 1244], [149, 618, 1243], [149, 619, 1242], [149, 622, 1239], [149, 623, 1238],
[149, 624, 1237], [162, 599, 1249], [162, 624, 1224], [163, 598, 1249], [163, 599, 1248],
[163, 623, 1224], [163, 624, 1223], [164, 597, 1249], [164, 598, 1248], [164, 599, 1247],
[164, 622, 1224], [164, 623, 1223], [164, 624, 1222], [167, 594, 1249], [167, 599, 1244],
[167, 619, 1224], [167, 624, 1219], [168, 593, 1249], [168, 594, 1248], [168, 598, 1244],
[168, 599, 1243], [168, 618, 1224], [168, 619, 1223], [168, 623, 1219], [168, 624, 1218],
[169, 592, 1249], [169, 593, 1248], [169, 594, 1247], [169, 597, 1244], [169, 598, 1243],
[169, 599, 1242], [169, 617, 1224], [169, 618, 1223], [169, 619, 1222], [169, 622, 1219],
[169, 623, 1218], [169, 624, 1217], [172, 589, 1249], [172, 594, 1244], [172, 599, 1239],
[172, 614, 1224], [172, 619, 1219], [172, 624, 1214], [173, 588, 1249], [173, 589, 1248],
[173, 593, 1244], [173, 594, 1243], [173, 598, 1239], [173, 599, 1238], [173, 613, 1224],
[173, 614, 1223], [173, 618, 1219], [173, 619, 1218], [173, 623, 1214], [173, 624, 1213],
[174, 587, 1249], [174, 588, 1248], [174, 589, 1247], [174, 592, 1244], [174, 593, 1243],
[174, 594, 1242], [174, 597, 1239], [174, 598, 1238], [174, 599, 1237], [174, 612, 1224],
[174, 613, 1223], [174, 614, 1222], [174, 617, 1219], [174, 618, 1218], [174, 619, 1217],
[174, 622, 1214], [174, 623, 1213], [174, 624, 1212], [187, 574, 1249], [187, 599, 1224],
[187, 624, 1199], [188, 573, 1249], [188, 574, 1248], [188, 598, 1224], [188, 599, 1223],
[188, 623, 1199], [188, 624, 1198], [189, 572, 1249], [189, 573, 1248], [189, 574, 1247],
[189, 597, 1224], [189, 598, 1223], [189, 599, 1222], [189, 622, 1199], [189, 623, 1198],
[189, 624, 1197], [192, 569, 1249], [192, 574, 1244], [192, 594, 1224], [192, 599, 1219],
[192, 619, 1199], [192, 624, 1194], [193, 568, 1249], [193, 569, 1248], [193, 573, 1244],
[193, 574, 1243], [193, 593, 1224], [193, 594, 1223], [193, 598, 1219], [193, 599, 1218],
[193, 618, 1199], [193, 619, 1198], [193, 623, 1194], [193, 624, 1193], [194, 567, 1249],
[194, 568, 1248], [194, 569, 1247], [194, 572, 1244], [194, 573, 1243], [194, 574, 1242],
[194, 592, 1224], [194, 593, 1223], [194, 594, 1222], [194, 597, 1219], [194, 598, 1218],
[194, 599, 1217], [194, 617, 1199], [194, 618, 1198], [194, 619, 1197], [194, 622, 1194],
[194, 623, 1193], [194, 624, 1192], [197, 564, 1249], [197, 569, 1244], [197, 574, 1239],
[197, 589, 1224], [197, 594, 1219], [197, 599, 1214], [197, 614, 1199], [197, 619, 1194],
[197, 624, 1189], [198, 563, 1249], [198, 564, 1248], [198, 568, 1244], [198, 569, 1243],
[198, 573, 1239], [198, 574, 1238], [198, 588, 1224], [198, 589, 1223], [198, 593, 1219],
[198, 594, 1218], [198, 598, 1214], [198, 599, 1213], [198, 613, 1199], [198, 614, 1198],
[198, 618, 1194], [198, 619, 1193], [198, 623, 1189], [198, 624, 1188], [199, 562, 1249],
[199, 563, 1248], [199, 564, 1247], [199, 567, 1244], [199, 568, 1243], [199, 569, 1242],
[199, 572, 1239], [199, 573, 1238], [199, 574, 1237], [199, 587, 1224], [199, 588, 1223],
[199, 589, 1222], [199, 592, 1219], [199, 593, 1218], [199, 594, 1217], [199, 597, 1214],
[199, 598, 1213], [199, 599, 1212], [199, 612, 1199], [199, 613, 1198], [199, 614, 1197],
[199, 617, 1194], [199, 618, 1193], [199, 619, 1192], [199, 622, 1189], [199, 623, 1188],
[199, 624, 1187], [212, 549, 1249], [212, 574, 1224], [212, 599, 1199], [212, 624, 1174],
[213, 548, 1249], [213, 549, 1248], [213, 573, 1224], [213, 574, 1223], [213, 598, 1199],
[213, 599, 1198], [213, 623, 1174], [213, 624, 1173], [214, 547, 1249], [214, 548, 1248],
[214, 549, 1247], [214, 572, 1224], [214, 573, 1223], [214, 574, 1222], [214, 597, 1199],
[214, 598, 1198], [214, 599, 1197], [214, 622, 1174], [214, 623, 1173], [214, 624, 1172],
[217, 544, 1249], [217, 549, 1244], [217, 569, 1224], [217, 574, 1219], [217, 594, 1199],
[217, 599, 1194], [217, 619, 1174], [217, 624, 1169], [218, 543, 1249], [218, 544, 1248],
[218, 548, 1244], [218, 549, 1243], [218, 568, 1224], [218, 569, 1223], [218, 573, 1219],
[218, 574, 1218], [218, 593, 1199], [218, 594, 1198], [218, 598, 1194], [218, 599, 1193],
[218, 618, 1174], [218, 619, 1173], [218, 623, 1169], [218, 624, 1168], [219, 542, 1249],
[219, 543, 1248], [219, 544, 1247], [219, 547, 1244], [219, 548, 1243], [219, 549, 1242],
[219, 567, 1224], [219, 568, 1223], [219, 569, 1222], [219, 572, 1219], [219, 573, 1218],
[219, 574, 1217], [219, 592, 1199], [219, 593, 1198], [219, 594, 1197], [219, 597, 1194],
[219, 598, 1193], [219, 599, 1192], [219, 617, 1174], [219, 618, 1173], [219, 619, 1172],
[219, 622, 1169], [219, 623, 1168], [219, 624, 1167], [222, 539, 1249], [222, 544, 1244],
[222, 549, 1239], [222, 564, 1224], [222, 569, 1219], [222, 574, 1214], [222, 589, 1199],
[222, 594, 1194], [222, 599, 1189], [222, 614, 1174], [222, 619, 1169], [222, 624, 1164],
[223, 538, 1249], [223, 539, 1248], [223, 543, 1244], [223, 544, 1243], [223, 548, 1239],
[223, 549, 1238], [223, 563, 1224], [223, 564, 1223], [223, 568, 1219], [223, 569, 1218],
[223, 573, 1214], [223, 574, 1213], [223, 588, 1199], [223, 589, 1198], [223, 593, 1194],
[223, 594, 1193], [223, 598, 1189], [223, 599, 1188], [223, 613, 1174], [223, 614, 1173],
[223, 618, 1169], [223, 619, 1168], [223, 623, 1164], [223, 624, 1163], [224, 537, 1249],
[224, 538, 1248], [224, 539, 1247], [224, 542, 1244], [224, 543, 1243], [224, 544, 1242],
[224, 547, 1239], [224, 548, 1238], [224, 549, 1237], [224, 562, 1224], [224, 563, 1223],
[224, 564, 1222], [224, 567, 1219], [224, 568, 1218], [224, 569, 1217], [224, 572, 1214],
[224, 573, 1213], [224, 574, 1212], [224, 587, 1199], [224, 588, 1198], [224, 589, 1197],
[224, 592, 1194], [224, 593, 1193], [224, 594, 1192], [224, 597, 1189], [224, 598, 1188],
[224, 599, 1187], [224, 612, 1174], [224, 613, 1173], [224, 614, 1172], [224, 617, 1169],
[224, 618, 1168], [224, 619, 1167], [224, 622, 1164], [224, 623, 1163], [224, 624, 1162],
[237, 524, 1249], [237, 549, 1224], [237, 574, 1199], [237, 599, 1174], [237, 624, 1149],
[238, 523, 1249], [238, 524, 1248], [238, 548, 1224], [238, 549, 1223], [238, 573, 1199],
[238, 574, 1198], [238, 598, 1174], [238, 599, 1173], [238, 623, 1149], [238, 624, 1148],
[239, 522, 1249], [239, 523, 1248], [239, 524, 1247], [239, 547, 1224], [239, 548, 1223],
[239, 549, 1222], [239, 572, 1199], [239, 573, 1198], [239, 574, 1197], [239, 597, 1174],
[239, 598, 1173], [239, 599, 1172], [239, 622, 1149], [239, 623, 1148], [239, 624, 1147],
[242, 519, 1249], [242, 524, 1244], [242, 544, 1224], [242, 549, 1219], [242, 569, 1199],
[242, 574, 1194], [242, 594, 1174], [242, 599, 1169], [242, 619, 1149], [242, 624, 1144],
[243, 518, 1249], [243, 519, 1248], [243, 523, 1244], [243, 524, 1243], [243, 543, 1224],
[243, 544, 1223], [243, 548, 1219], [243, 549, 1218], [243, 568, 1199], [243, 569, 1198],
[243, 573, 1194], [243, 574, 1193], [243, 593, 1174], [243, 594, 1173], [243, 598, 1169],
[243, 599, 1168], [243, 618, 1149], [243, 619, 1148], [243, 623, 1144], [243, 624, 1143],
[244, 517, 1249], [244, 518, 1248], [244, 519, 1247], [244, 522, 1244], [244, 523, 1243],
[244, 524, 1242], [244, 542, 1224], [244, 543, 1223], [244, 544, 1222], [244, 547, 1219],
[244, 548, 1218], [244, 549, 1217], [244, 567, 1199], [244, 568, 1198], [244, 569, 1197],
[244, 572, 1194], [244, 573, 1193], [244, 574, 1192], [244, 592, 1174], [244, 593, 1173],
[244, 594, 1172], [244, 597, 1169], [244, 598, 1168], [244, 599, 1167], [244, 617, 1149],
[244, 618, 1148], [244, 619, 1147], [244, 622, 1144], [244, 623, 1143], [244, 624, 1142],
[247, 514, 1249], [247, 519, 1244], [247, 524, 1239], [247, 539, 1224], [247, 544, 1219],
[247, 549, 1214], [247, 564, 1199], [247, 569, 1194], [247, 574, 1189], [247, 589, 1174],
[247, 594, 1169], [247, 599, 1164], [247, 614, 1149], [247, 619, 1144], [247, 624, 1139],
[248, 513, 1249], [248, 514, 1248], [248, 518, 1244], [248, 519, 1243], [248, 523, 1239],
[248, 524, 1238], [248, 538, 1224], [248, 539, 1223], [248, 543, 1219], [248, 544, 1218],
[248, 548, 1214], [248, 549, 1213], [248, 563, 1199], [248, 564, 1198], [248, 568, 1194],
[248, 569, 1193], [248, 573, 1189], [248, 574, 1188], [248, 588, 1174], [248, 589, 1173],
[248, 593, 1169], [248, 594, 1168], [248, 598, 1164], [248, 599, 1163], [248, 613, 1149],
[248, 614, 1148], [248, 618, 1144], [248, 619, 1143], [248, 623, 1139], [248, 624, 1138],
[249, 512, 1249], [249, 513, 1248], [249, 514, 1247], [249, 517, 1244], [249, 518, 1243],
[249, 519, 1242], [249, 522, 1239], [249, 523, 1238], [249, 524, 1237], [249, 537, 1224],
[249, 538, 1223], [249, 539, 1222], [249, 542, 1219], [249, 543, 1218], [249, 544, 1217],
[249, 547, 1214], [249, 548, 1213], [249, 549, 1212], [249, 562, 1199], [249, 563, 1198],
[249, 564, 1197], [249, 567, 1194], [249, 568, 1193], [249, 569, 1192], [249, 572, 1189],
[249, 573, 1188], [249, 574, 1187], [249, 587, 1174], [249, 588, 1173], [249, 589, 1172],
[249, 592, 1169], [249, 593, 1168], [249, 594, 1167], [249, 597, 1164], [249, 598, 1163],
[249, 599, 1162], [249, 612, 1149], [249, 613, 1148], [249, 614, 1147], [249, 617, 1144],
[249, 618, 1143], [249, 619, 1142], [249, 622, 1139], [249, 623, 1138], [249, 624, 1137],
[262, 499, 1249], [262, 624, 1124], [263, 498, 1249], [263, 499, 1248], [263, 623, 1124],
[263, 624, 1123], [264, 497, 1249], [264, 498, 1248], [264, 499, 1247], [264, 622, 1124],
[264, 623, 1123], [264, 624, 1122], [267, 494, 1249], [267, 499, 1244], [267, 619, 1124],
[267, 624, 1119], [268, 493, 1249], [268, 494, 1248], [268, 498, 1244], [268, 499, 1243],
[268, 618, 1124], [268, 619, 1123], [268, 623, 1119], [268, 624, 1118], [269, 492, 1249],
[269, 493, 1248], [269, 494, 1247], [269, 497, 1244], [269, 498, 1243], [269, 499, 1242],
[269, 617, 1124], [269, 618, 1123], [269, 619, 1122], [269, 622, 1119], [269, 623, 1118],
[269, 624, 1117], [272, 489, 1249], [272, 494, 1244], [272, 499, 1239], [272, 614, 1124],
[272, 619, 1119], [272, 624, 1114], [273, 488, 1249], [273, 489, 1248], [273, 493, 1244],
[273, 494, 1243], [273, 498, 1239], [273, 499, 1238], [273, 613, 1124], [273, 614, 1123],
[273, 618, 1119], [273, 619, 1118], [273, 623, 1114], [273, 624, 1113], [274, 487, 1249],
[274, 488, 1248], [274, 489, 1247], [274, 492, 1244], [274, 493, 1243], [274, 494, 1242],
[274, 497, 1239], [274, 498, 1238], [274, 499, 1237], [274, 612, 1124], [274, 613, 1123],
[274, 614, 1122], [274, 617, 1119], [274, 618, 1118], [274, 619, 1117], [274, 622, 1114],
[274, 623, 1113], [274, 624, 1112], [287, 474, 1249], [287, 499, 1224], [287, 599, 1124],
[287, 624, 1099], [288, 473, 1249], [288, 474, 1248], [288, 498, 1224], [288, 499, 1223],
[288, 598, 1124], [288, 599, 1123], [288, 623, 1099], [288, 624, 1098], [289, 472, 1249],
[289, 473, 1248], [289, 474, 1247], [289, 497, 1224], [289, 498, 1223], [289, 499, 1222],
[289, 597, 1124], [289, 598, 1123], [289, 599, 1122], [289, 622, 1099], [289, 623, 1098],
[289, 624, 1097], [292, 469, 1249], [292, 474, 1244], [292, 494, 1224], [292, 499, 1219],
[292, 594, 1124], [292, 599, 1119], [292, 619, 1099], [292, 624, 1094], [293, 468, 1249],
[293, 469, 1248], [293, 473, 1244], [293, 474, 1243], [293, 493, 1224], [293, 494, 1223],
[293, 498, 1219], [293, 499, 1218], [293, 593, 1124], [293, 594, 1123], [293, 598, 1119],
[293, 599, 1118], [293, 618, 1099], [293, 619, 1098], [293, 623, 1094], [293, 624, 1093],
[294, 467, 1249], [294, 468, 1248], [294, 469, 1247], [294, 472, 1244], [294, 473, 1243],
[294, 474, 1242], [294, 492, 1224], [294, 493, 1223], [294, 494, 1222], [294, 497, 1219],
[294, 498, 1218], [294, 499, 1217], [294, 592, 1124], [294, 593, 1123], [294, 594, 1122],
[294, 597, 1119], [294, 598, 1118], [294, 599, 1117], [294, 617, 1099], [294, 618, 1098],
[294, 619, 1097], [294, 622, 1094], [294, 623, 1093], [294, 624, 1092], [297, 464, 1249],
[297, 469, 1244], [297, 474, 1239], [297, 489, 1224], [297, 494, 1219], [297, 499, 1214],
[297, 589, 1124], [297, 594, 1119], [297, 599, 1114], [297, 614, 1099], [297, 619, 1094],
[297, 624, 1089], [298, 463, 1249], [298, 464, 1248], [298, 468, 1244], [298, 469, 1243],
[298, 473, 1239], [298, 474, 1238], [298, 488, 1224], [298, 489, 1223], [298, 493, 1219],
[298, 494, 1218], [298, 498, 1214], [298, 499, 1213], [298, 588, 1124], [298, 589, 1123],
[298, 593, 1119], [298, 594, 1118], [298, 598, 1114], [298, 599, 1113], [298, 613, 1099],
[298, 614, 1098], [298, 618, 1094], [298, 619, 1093], [298, 623, 1089], [298, 624, 1088],
[299, 462, 1249], [299, 463, 1248], [299, 464, 1247], [299, 467, 1244], [299, 468, 1243],
[299, 469, 1242], [299, 472, 1239], [299, 473, 1238], [299, 474, 1237], [299, 487, 1224],
[299, 488, 1223], [299, 489, 1222], [299, 492, 1219], [299, 493, 1218], [299, 494, 1217],
[299, 497, 1214], [299, 498, 1213], [299, 499, 1212], [299, 587, 1124], [299, 588, 1123],
[299, 589, 1122], [299, 592, 1119], [299, 593, 1118], [299, 594, 1117], [299, 597, 1114],
[299, 598, 1113], [299, 599, 1112], [299, 612, 1099], [299, 613, 1098], [299, 614, 1097],
[299, 617, 1094], [299, 618, 1093], [299, 619, 1092], [299, 622, 1089], [299, 623, 1088],
[299, 624, 1087], [312, 449, 1249], [312, 474, 1224], [312, 499, 1199], [312, 574, 1124],
[312, 599, 1099], [312, 624, 1074], [313, 448, 1249], [313, 449, 1248], [313, 473, 1224],
[313, 474, 1223], [313, 498, 1199], [313, 499, 1198], [313, 573, 1124], [313, 574, 1123],
[313, 598, 1099], [313, 599, 1098], [313, 623, 1074], [313, 624, 1073], [314, 447, 1249],
[314, 448, 1248], [314, 449, 1247], [314, 472, 1224], [314, 473, 1223], [314, 474, 1222],
[314, 497, 1199], [314, 498, 1198], [314, 499, 1197], [314, 572, 1124], [314, 573, 1123],
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[374, 599, 1037], [374, 612, 1024], [374, 613, 1023], [374, 614, 1022], [374, 617, 1019],
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[388, 624, 998], [389, 497, 1124], [389, 498, 1123], [389, 499, 1122], [389, 622, 999],
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[392, 624, 994], [393, 493, 1124], [393, 494, 1123], [393, 498, 1119], [393, 499, 1118],
[393, 618, 999], [393, 619, 998], [393, 623, 994], [393, 624, 993], [394, 492, 1124],
[394, 493, 1123], [394, 494, 1122], [394, 497, 1119], [394, 498, 1118], [394, 499, 1117],
[394, 617, 999], [394, 618, 998], [394, 619, 997], [394, 622, 994], [394, 623, 993],
[394, 624, 992], [397, 489, 1124], [397, 494, 1119], [397, 499, 1114], [397, 614, 999],
[397, 619, 994], [397, 624, 989], [398, 488, 1124], [398, 489, 1123], [398, 493, 1119],
[398, 494, 1118], [398, 498, 1114], [398, 499, 1113], [398, 613, 999], [398, 614, 998],
[398, 618, 994], [398, 619, 993], [398, 623, 989], [398, 624, 988], [399, 487, 1124],
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[399, 497, 1114], [399, 498, 1113], [399, 499, 1112], [399, 612, 999], [399, 613, 998],
[399, 614, 997], [399, 617, 994], [399, 618, 993], [399, 619, 992], [399, 622, 989],
[399, 623, 988], [399, 624, 987], [412, 474, 1124], [412, 499, 1099], [412, 599, 999],
[412, 624, 974], [413, 473, 1124], [413, 474, 1123], [413, 498, 1099], [413, 499, 1098],
[413, 598, 999], [413, 599, 998], [413, 623, 974], [413, 624, 973], [414, 472, 1124],
[414, 473, 1123], [414, 474, 1122], [414, 497, 1099], [414, 498, 1098], [414, 499, 1097],
[414, 597, 999], [414, 598, 998], [414, 599, 997], [414, 622, 974], [414, 623, 973],
[414, 624, 972], [417, 469, 1124], [417, 474, 1119], [417, 494, 1099], [417, 499, 1094],
[417, 594, 999], [417, 599, 994], [417, 619, 974], [417, 624, 969], [418, 468, 1124],
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[418, 498, 1094], [418, 499, 1093], [418, 593, 999], [418, 594, 998], [418, 598, 994],
[418, 599, 993], [418, 618, 974], [418, 619, 973], [418, 623, 969], [418, 624, 968],
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[419, 619, 972], [419, 622, 969], [419, 623, 968], [419, 624, 967], [422, 464, 1124],
[422, 469, 1119], [422, 474, 1114], [422, 489, 1099], [422, 494, 1094], [422, 499, 1089],
[422, 589, 999], [422, 594, 994], [422, 599, 989], [422, 614, 974], [422, 619, 969],
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[423, 614, 973], [423, 618, 969], [423, 619, 968], [423, 623, 964], [423, 624, 963],
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[424, 497, 1089], [424, 498, 1088], [424, 499, 1087], [424, 587, 999], [424, 588, 998],
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[424, 617, 969], [424, 618, 968], [424, 619, 967], [424, 622, 964], [424, 623, 963],
[424, 624, 962], [437, 449, 1124], [437, 474, 1099], [437, 499, 1074], [437, 574, 999],
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[439, 448, 1123], [439, 449, 1122], [439, 472, 1099], [439, 473, 1098], [439, 474, 1097],
[439, 497, 1074], [439, 498, 1073], [439, 499, 1072], [439, 572, 999], [439, 573, 998],
[439, 574, 997], [439, 597, 974], [439, 598, 973], [439, 599, 972], [439, 622, 949],
[439, 623, 948], [439, 624, 947], [442, 444, 1124], [442, 449, 1119], [442, 469, 1099],
[442, 474, 1094], [442, 494, 1074], [442, 499, 1069], [442, 569, 999], [442, 574, 994],
[442, 594, 974], [442, 599, 969], [442, 619, 949], [442, 624, 944], [443, 443, 1124],
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[443, 473, 1094], [443, 474, 1093], [443, 493, 1074], [443, 494, 1073], [443, 498, 1069],
[443, 499, 1068], [443, 568, 999], [443, 569, 998], [443, 573, 994], [443, 574, 993],
[443, 593, 974], [443, 594, 973], [443, 598, 969], [443, 599, 968], [443, 618, 949],
[443, 619, 948], [443, 623, 944], [443, 624, 943], [444, 444, 1122], [444, 447, 1119],
[444, 448, 1118], [444, 449, 1117], [444, 467, 1099], [444, 468, 1098], [444, 469, 1097],
[444, 472, 1094], [444, 473, 1093], [444, 474, 1092], [444, 492, 1074], [444, 493, 1073],
[444, 494, 1072], [444, 497, 1069], [444, 498, 1068], [444, 499, 1067], [444, 567, 999],
[444, 568, 998], [444, 569, 997], [444, 572, 994], [444, 573, 993], [444, 574, 992],
[444, 592, 974], [444, 593, 973], [444, 594, 972], [444, 597, 969], [444, 598, 968],
[444, 599, 967], [444, 617, 949], [444, 618, 948], [444, 619, 947], [444, 622, 944],
[444, 623, 943], [444, 624, 942], [447, 449, 1114], [447, 464, 1099], [447, 469, 1094],
[447, 474, 1089], [447, 489, 1074], [447, 494, 1069], [447, 499, 1064], [447, 564, 999],
[447, 569, 994], [447, 574, 989], [447, 589, 974], [447, 594, 969], [447, 599, 964],
[447, 614, 949], [447, 619, 944], [447, 624, 939], [448, 448, 1114], [448, 449, 1113],
[448, 463, 1099], [448, 464, 1098], [448, 468, 1094], [448, 469, 1093], [448, 473, 1089],
[448, 474, 1088], [448, 488, 1074], [448, 489, 1073], [448, 493, 1069], [448, 494, 1068],
[448, 498, 1064], [448, 499, 1063], [448, 563, 999], [448, 564, 998], [448, 568, 994],
[448, 569, 993], [448, 573, 989], [448, 574, 988], [448, 588, 974], [448, 589, 973],
[448, 593, 969], [448, 594, 968], [448, 598, 964], [448, 599, 963], [448, 613, 949],
[448, 614, 948], [448, 618, 944], [448, 619, 943], [448, 623, 939], [448, 624, 938],
[449, 449, 1112], [449, 462, 1099], [449, 463, 1098], [449, 464, 1097], [449, 467, 1094],
[449, 468, 1093], [449, 469, 1092], [449, 472, 1089], [449, 473, 1088], [449, 474, 1087],
[449, 487, 1074], [449, 488, 1073], [449, 489, 1072], [449, 492, 1069], [449, 493, 1068],
[449, 494, 1067], [449, 497, 1064], [449, 498, 1063], [449, 499, 1062], [449, 562, 999],
[449, 563, 998], [449, 564, 997], [449, 567, 994], [449, 568, 993], [449, 569, 992],
[449, 572, 989], [449, 573, 988], [449, 574, 987], [449, 587, 974], [449, 588, 973],
[449, 589, 972], [449, 592, 969], [449, 593, 968], [449, 594, 967], [449, 597, 964],
[449, 598, 963], [449, 599, 962], [449, 612, 949], [449, 613, 948], [449, 614, 947],
[449, 617, 944], [449, 618, 943], [449, 619, 942], [449, 622, 939], [449, 623, 938],
[449, 624, 937], [462, 474, 1074], [462, 499, 1049], [462, 549, 999], [462, 574, 974],
[462, 599, 949], [462, 624, 924], [463, 473, 1074], [463, 474, 1073], [463, 498, 1049],
[463, 499, 1048], [463, 548, 999], [463, 549, 998], [463, 573, 974], [463, 574, 973],
[463, 598, 949], [463, 599, 948], [463, 623, 924], [463, 624, 923], [464, 472, 1074],
[464, 473, 1073], [464, 474, 1072], [464, 497, 1049], [464, 498, 1048], [464, 499, 1047],
[464, 547, 999], [464, 548, 998], [464, 549, 997], [464, 572, 974], [464, 573, 973],
[464, 574, 972], [464, 597, 949], [464, 598, 948], [464, 599, 947], [464, 622, 924],
[464, 623, 923], [464, 624, 922], [467, 469, 1074], [467, 474, 1069], [467, 494, 1049],
[467, 499, 1044], [467, 544, 999], [467, 549, 994], [467, 569, 974], [467, 574, 969],
[467, 594, 949], [467, 599, 944], [467, 619, 924], [467, 624, 919], [468, 468, 1074],
[468, 469, 1073], [468, 473, 1069], [468, 474, 1068], [468, 493, 1049], [468, 494, 1048],
[468, 498, 1044], [468, 499, 1043], [468, 543, 999], [468, 544, 998], [468, 548, 994],
[468, 549, 993], [468, 568, 974], [468, 569, 973], [468, 573, 969], [468, 574, 968],
[468, 593, 949], [468, 594, 948], [468, 598, 944], [468, 599, 943], [468, 618, 924],
[468, 619, 923], [468, 623, 919], [468, 624, 918], [469, 469, 1072], [469, 472, 1069],
[469, 473, 1068], [469, 474, 1067], [469, 492, 1049], [469, 493, 1048], [469, 494, 1047],
[469, 497, 1044], [469, 498, 1043], [469, 499, 1042], [469, 542, 999], [469, 543, 998],
[469, 544, 997], [469, 547, 994], [469, 548, 993], [469, 549, 992], [469, 567, 974],
[469, 568, 973], [469, 569, 972], [469, 572, 969], [469, 573, 968], [469, 574, 967],
[469, 592, 949], [469, 593, 948], [469, 594, 947], [469, 597, 944], [469, 598, 943],
[469, 599, 942], [469, 617, 924], [469, 618, 923], [469, 619, 922], [469, 622, 919],
[469, 623, 918], [469, 624, 917], [472, 474, 1064], [472, 489, 1049], [472, 494, 1044],
[472, 499, 1039], [472, 539, 999], [472, 544, 994], [472, 549, 989], [472, 564, 974],
[472, 569, 969], [472, 574, 964], [472, 589, 949], [472, 594, 944], [472, 599, 939],
[472, 614, 924], [472, 619, 919], [472, 624, 914], [473, 473, 1064], [473, 474, 1063],
[473, 488, 1049], [473, 489, 1048], [473, 493, 1044], [473, 494, 1043], [473, 498, 1039],
[473, 499, 1038], [473, 538, 999], [473, 539, 998], [473, 543, 994], [473, 544, 993],
[473, 548, 989], [473, 549, 988], [473, 563, 974], [473, 564, 973], [473, 568, 969],
[473, 569, 968], [473, 573, 964], [473, 574, 963], [473, 588, 949], [473, 589, 948],
[473, 593, 944], [473, 594, 943], [473, 598, 939], [473, 599, 938], [473, 613, 924],
[473, 614, 923], [473, 618, 919], [473, 619, 918], [473, 623, 914], [473, 624, 913],
[474, 474, 1062], [474, 487, 1049], [474, 488, 1048], [474, 489, 1047], [474, 492, 1044],
[474, 493, 1043], [474, 494, 1042], [474, 497, 1039], [474, 498, 1038], [474, 499, 1037],
[474, 537, 999], [474, 538, 998], [474, 539, 997], [474, 542, 994], [474, 543, 993],
[474, 544, 992], [474, 547, 989], [474, 548, 988], [474, 549, 987], [474, 562, 974],
[474, 563, 973], [474, 564, 972], [474, 567, 969], [474, 568, 968], [474, 569, 967],
[474, 572, 964], [474, 573, 963], [474, 574, 962], [474, 587, 949], [474, 588, 948],
[474, 589, 947], [474, 592, 944], [474, 593, 943], [474, 594, 942], [474, 597, 939],
[474, 598, 938], [474, 599, 937], [474, 612, 924], [474, 613, 923], [474, 614, 922],
[474, 617, 919], [474, 618, 918], [474, 619, 917], [474, 622, 914], [474, 623, 913],
[474, 624, 912], [487, 499, 1024], [487, 524, 999], [487, 549, 974], [487, 574, 949],
[487, 599, 924], [487, 624, 899], [488, 498, 1024], [488, 499, 1023], [488, 523, 999],
[488, 524, 998], [488, 548, 974], [488, 549, 973], [488, 573, 949], [488, 574, 948],
[488, 598, 924], [488, 599, 923], [488, 623, 899], [488, 624, 898], [489, 497, 1024],
[489, 498, 1023], [489, 499, 1022], [489, 522, 999], [489, 523, 998], [489, 524, 997],
[489, 547, 974], [489, 548, 973], [489, 549, 972], [489, 572, 949], [489, 573, 948],
[489, 574, 947], [489, 597, 924], [489, 598, 923], [489, 599, 922], [489, 622, 899],
[489, 623, 898], [489, 624, 897], [492, 494, 1024], [492, 499, 1019], [492, 519, 999],
[492, 524, 994], [492, 544, 974], [492, 549, 969], [492, 569, 949], [492, 574, 944],
[492, 594, 924], [492, 599, 919], [492, 619, 899], [492, 624, 894], [493, 493, 1024],
[493, 494, 1023], [493, 498, 1019], [493, 499, 1018], [493, 518, 999], [493, 519, 998],
[493, 523, 994], [493, 524, 993], [493, 543, 974], [493, 544, 973], [493, 548, 969],
[493, 549, 968], [493, 568, 949], [493, 569, 948], [493, 573, 944], [493, 574, 943],
[493, 593, 924], [493, 594, 923], [493, 598, 919], [493, 599, 918], [493, 618, 899],
[493, 619, 898], [493, 623, 894], [493, 624, 893], [494, 494, 1022], [494, 497, 1019],
[494, 498, 1018], [494, 499, 1017], [494, 517, 999], [494, 518, 998], [494, 519, 997],
[494, 522, 994], [494, 523, 993], [494, 524, 992], [494, 542, 974], [494, 543, 973],
[494, 544, 972], [494, 547, 969], [494, 548, 968], [494, 549, 967], [494, 567, 949],
[494, 568, 948], [494, 569, 947], [494, 572, 944], [494, 573, 943], [494, 574, 942],
[494, 592, 924], [494, 593, 923], [494, 594, 922], [494, 597, 919], [494, 598, 918],
[494, 599, 917], [494, 617, 899], [494, 618, 898], [494, 619, 897], [494, 622, 894],
[494, 623, 893], [494, 624, 892], [497, 499, 1014], [497, 514, 999], [497, 519, 994],
[497, 524, 989], [497, 539, 974], [497, 544, 969], [497, 549, 964], [497, 564, 949],
[497, 569, 944], [497, 574, 939], [497, 589, 924], [497, 594, 919], [497, 599, 914],
[497, 614, 899], [497, 619, 894], [497, 624, 889], [498, 498, 1014], [498, 499, 1013],
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[498, 524, 988], [498, 538, 974], [498, 539, 973], [498, 543, 969], [498, 544, 968],
[498, 548, 964], [498, 549, 963], [498, 563, 949], [498, 564, 948], [498, 568, 944],
[498, 569, 943], [498, 573, 939], [498, 574, 938], [498, 588, 924], [498, 589, 923],
[498, 593, 919], [498, 594, 918], [498, 598, 914], [498, 599, 913], [498, 613, 899],
[498, 614, 898], [498, 618, 894], [498, 619, 893], [498, 623, 889], [498, 624, 888],
[499, 499, 1012], [499, 512, 999], [499, 513, 998], [499, 514, 997], [499, 517, 994],
[499, 518, 993], [499, 519, 992], [499, 522, 989], [499, 523, 988], [499, 524, 987],
[499, 537, 974], [499, 538, 973], [499, 539, 972], [499, 542, 969], [499, 543, 968],
[499, 544, 967], [499, 547, 964], [499, 548, 963], [499, 549, 962], [499, 562, 949],
[499, 563, 948], [499, 564, 947], [499, 567, 944], [499, 568, 943], [499, 569, 942],
[499, 572, 939], [499, 573, 938], [499, 574, 937], [499, 587, 924], [499, 588, 923],
[499, 589, 922], [499, 592, 919], [499, 593, 918], [499, 594, 917], [499, 597, 914],
[499, 598, 913], [499, 599, 912], [499, 612, 899], [499, 613, 898], [499, 614, 897],
[499, 617, 894], [499, 618, 893], [499, 619, 892], [499, 622, 889], [499, 623, 888],
[499, 624, 887], [512, 624, 874], [513, 623, 874], [513, 624, 873], [514, 622, 874],
[514, 623, 873], [514, 624, 872], [517, 619, 874], [517, 624, 869], [518, 618, 874],
[518, 619, 873], [518, 623, 869], [518, 624, 868], [519, 617, 874], [519, 618, 873],
[519, 619, 872], [519, 622, 869], [519, 623, 868], [519, 624, 867], [522, 614, 874],
[522, 619, 869], [522, 624, 864], [523, 613, 874], [523, 614, 873], [523, 618, 869],
[523, 619, 868], [523, 623, 864], [523, 624, 863], [524, 612, 874], [524, 613, 873],
[524, 614, 872], [524, 617, 869], [524, 618, 868], [524, 619, 867], [524, 622, 864],
[524, 623, 863], [524, 624, 862], [537, 599, 874], [537, 624, 849], [538, 598, 874],
[538, 599, 873], [538, 623, 849], [538, 624, 848], [539, 597, 874], [539, 598, 873],
[539, 599, 872], [539, 622, 849], [539, 623, 848], [539, 624, 847], [542, 594, 874],
[542, 599, 869], [542, 619, 849], [542, 624, 844], [543, 593, 874], [543, 594, 873],
[543, 598, 869], [543, 599, 868], [543, 618, 849], [543, 619, 848], [543, 623, 844],
[543, 624, 843], [544, 592, 874], [544, 593, 873], [544, 594, 872], [544, 597, 869],
[544, 598, 868], [544, 599, 867], [544, 617, 849], [544, 618, 848], [544, 619, 847],
[544, 622, 844], [544, 623, 843], [544, 624, 842], [547, 589, 874], [547, 594, 869],
[547, 599, 864], [547, 614, 849], [547, 619, 844], [547, 624, 839], [548, 588, 874],
[548, 589, 873], [548, 593, 869], [548, 594, 868], [548, 598, 864], [548, 599, 863],
[548, 613, 849], [548, 614, 848], [548, 618, 844], [548, 619, 843], [548, 623, 839],
[548, 624, 838], [549, 587, 874], [549, 588, 873], [549, 589, 872], [549, 592, 869],
[549, 593, 868], [549, 594, 867], [549, 597, 864], [549, 598, 863], [549, 599, 862],
[549, 612, 849], [549, 613, 848], [549, 614, 847], [549, 617, 844], [549, 618, 843],
[549, 619, 842], [549, 622, 839], [549, 623, 838], [549, 624, 837], [562, 574, 874],
[562, 599, 849], [562, 624, 824], [563, 573, 874], [563, 574, 873], [563, 598, 849],
[563, 599, 848], [563, 623, 824], [563, 624, 823], [564, 572, 874], [564, 573, 873],
[564, 574, 872], [564, 597, 849], [564, 598, 848], [564, 599, 847], [564, 622, 824],
[564, 623, 823], [564, 624, 822], [567, 569, 874], [567, 574, 869], [567, 594, 849],
[567, 599, 844], [567, 619, 824], [567, 624, 819], [568, 568, 874], [568, 569, 873],
[568, 573, 869], [568, 574, 868], [568, 593, 849], [568, 594, 848], [568, 598, 844],
[568, 599, 843], [568, 618, 824], [568, 619, 823], [568, 623, 819], [568, 624, 818],
[569, 569, 872], [569, 572, 869], [569, 573, 868], [569, 574, 867], [569, 592, 849],
[569, 593, 848], [569, 594, 847], [569, 597, 844], [569, 598, 843], [569, 599, 842],
[569, 617, 824], [569, 618, 823], [569, 619, 822], [569, 622, 819], [569, 623, 818],
[569, 624, 817], [572, 574, 864], [572, 589, 849], [572, 594, 844], [572, 599, 839],
[572, 614, 824], [572, 619, 819], [572, 624, 814], [573, 573, 864], [573, 574, 863],
[573, 588, 849], [573, 589, 848], [573, 593, 844], [573, 594, 843], [573, 598, 839],
[573, 599, 838], [573, 613, 824], [573, 614, 823], [573, 618, 819], [573, 619, 818],
[573, 623, 814], [573, 624, 813], [574, 574, 862], [574, 587, 849], [574, 588, 848],
[574, 589, 847], [574, 592, 844], [574, 593, 843], [574, 594, 842], [574, 597, 839],
[574, 598, 838], [574, 599, 837], [574, 612, 824], [574, 613, 823], [574, 614, 822],
[574, 617, 819], [574, 618, 818], [574, 619, 817], [574, 622, 814], [574, 623, 813],
[574, 624, 812], [587, 599, 824], [587, 624, 799], [588, 598, 824], [588, 599, 823],
[588, 623, 799], [588, 624, 798], [589, 597, 824], [589, 598, 823], [589, 599, 822],
[589, 622, 799], [589, 623, 798], [589, 624, 797], [592, 594, 824], [592, 599, 819],
[592, 619, 799], [592, 624, 794], [593, 593, 824], [593, 594, 823], [593, 598, 819],
[593, 599, 818], [593, 618, 799], [593, 619, 798], [593, 623, 794], [593, 624, 793],
[594, 594, 822], [594, 597, 819], [594, 598, 818], [594, 599, 817], [594, 617, 799],
[594, 618, 798], [594, 619, 797], [594, 622, 794], [594, 623, 793], [594, 624, 792],
[597, 599, 814], [597, 614, 799], [597, 619, 794], [597, 624, 789], [598, 598, 814],
[598, 599, 813], [598, 613, 799], [598, 614, 798], [598, 618, 794], [598, 619, 793],
[598, 623, 789], [598, 624, 788], [599, 599, 812], [599, 612, 799], [599, 613, 798],
[599, 614, 797], [599, 617, 794], [599, 618, 793], [599, 619, 792], [599, 622, 789],
[599, 623, 788], [599, 624, 787], [612, 624, 774], [613, 623, 774], [613, 624, 773],
[614, 622, 774], [614, 623, 773], [614, 624, 772], [617, 619, 774], [617, 624, 769],
[618, 618, 774], [618, 619, 773], [618, 623, 769], [618, 624, 768], [619, 619, 772],
[619, 622, 769], [619, 623, 768], [619, 624, 767], [622, 624, 764], [623, 623, 764],
[623, 624, 763], [624, 624, 762]

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 楼主| 发表于 2010-5-1 05:13 | 显示全部楼层

[分享][趣题征解] 2010 最小问题

当a,b,c 为整数且 1 ≤ a ≤ b ≤ c,a + b + c = 1 时,
a!b!c! 的 10-因子的个数等于 493 的概率是多少?
发表于 2010-10-19 22:48 | 显示全部楼层

[分享][趣题征解] 2010 最小问题

elimqiu不是笨蛋,不愚蠢,不驴打滚,不狗屎堆逻辑,elimqiu不是白痴,elimqiu不是饭桶,不是网痞,不是下三滥,
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