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[分享] 倒数之和为1

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数论爱好者
发表于 2011-9-11 19:19:09 | 显示全部楼层 |阅读模式

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有6个不同的自然数，它们的倒数之和为1，求这6个自然数
$1/{\(\ \ \)}+1/{\(\ \ \)}+1/{\(\ \ \)}+1/{\(\ \ \)}+1/{\(\ \ \)}+1/{\(\ \ \)}=1$
我是没有解出来，但现在我已经知道答案了
看看大家如何解，再公布答案
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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KeyTo9_Fans
发表于 2011-9-11 19:28:40 | 显示全部楼层
数字最大（或字典序最小）的解：

$1/2+1/3+1/7+1/43+1/1807+1/3263442=1$

不知道数字最小的解是多少。
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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数论爱好者
 楼主| 发表于 2011-9-12 00:09:50 | 显示全部楼层
1/2+1/3+1/9+1/27+1/81+1/162=1
1/2=1/3+1/6

1=1/2+1/3+1/6
=1/2+1/3+(1/3)*(1/3+1/6)
=1/2+1/3+1/9+(1/9)*(1/3+1/6)
=……
=1/2+1/3+1/9+1/27+1/81+1/162
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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gxqcn
发表于 2011-9-12 21:38:36 | 显示全部楼层
调出我十多年前用VB开发的《埃及分数分解》程序，设定“禁止重复真分数”及分解分数分母上限=162，得到的结果如下：
  1. No.1        1 = 1/2 + 1/3 + 1/7 + 1/96 + 1/140 + 1/160
  2. No.2        1 = 1/2 + 1/3 + 1/7 + 1/100 + 1/140 + 1/150
  3. No.3        1 = 1/2 + 1/3 + 1/7 + 1/108 + 1/135 + 1/140
  4. No.4        1 = 1/2 + 1/3 + 1/7 + 1/110 + 1/132 + 1/140
  5. No.5        1 = 1/2 + 1/3 + 1/7 + 1/112 + 1/126 + 1/144
  6. No.6        1 = 1/2 + 1/3 + 1/8 + 1/36 + 1/136 + 1/153
  7. No.7        1 = 1/2 + 1/3 + 1/8 + 1/38 + 1/114 + 1/152
  8. No.8        1 = 1/2 + 1/3 + 1/8 + 1/39 + 1/104 + 1/156
  9. No.9        1 = 1/2 + 1/3 + 1/8 + 1/39 + 1/120 + 1/130
  10. No.10        1 = 1/2 + 1/3 + 1/8 + 1/40 + 1/96 + 1/160
  11. No.11        1 = 1/2 + 1/3 + 1/8 + 1/40 + 1/100 + 1/150
  12. No.12        1 = 1/2 + 1/3 + 1/8 + 1/40 + 1/105 + 1/140
  13. No.13        1 = 1/2 + 1/3 + 1/8 + 1/40 + 1/108 + 1/135
  14. No.14        1 = 1/2 + 1/3 + 1/8 + 1/40 + 1/110 + 1/132
  15. No.15        1 = 1/2 + 1/3 + 1/8 + 1/42 + 1/88 + 1/154
  16. No.16        1 = 1/2 + 1/3 + 1/8 + 1/42 + 1/105 + 1/120
  17. No.17        1 = 1/2 + 1/3 + 1/8 + 1/44 + 1/88 + 1/132
  18. No.18        1 = 1/2 + 1/3 + 1/8 + 1/45 + 1/80 + 1/144
  19. No.19        1 = 1/2 + 1/3 + 1/8 + 1/45 + 1/90 + 1/120
  20. No.20        1 = 1/2 + 1/3 + 1/8 + 1/48 + 1/72 + 1/144
  21. No.21        1 = 1/2 + 1/3 + 1/8 + 1/48 + 1/80 + 1/120
  22. No.22        1 = 1/2 + 1/3 + 1/8 + 1/48 + 1/84 + 1/112
  23. No.23        1 = 1/2 + 1/3 + 1/8 + 1/50 + 1/75 + 1/120
  24. No.24        1 = 1/2 + 1/3 + 1/8 + 1/51 + 1/68 + 1/136
  25. No.25        1 = 1/2 + 1/3 + 1/8 + 1/52 + 1/72 + 1/117
  26. No.26        1 = 1/2 + 1/3 + 1/8 + 1/52 + 1/78 + 1/104
  27. No.27        1 = 1/2 + 1/3 + 1/8 + 1/54 + 1/72 + 1/108
  28. No.28        1 = 1/2 + 1/3 + 1/8 + 1/55 + 1/66 + 1/120
  29. No.29        1 = 1/2 + 1/3 + 1/8 + 1/56 + 1/60 + 1/140
  30. No.30        1 = 1/2 + 1/3 + 1/8 + 1/56 + 1/63 + 1/126
  31. No.31        1 = 1/2 + 1/3 + 1/8 + 1/56 + 1/70 + 1/105
  32. No.32        1 = 1/2 + 1/3 + 1/8 + 1/56 + 1/78 + 1/91
  33. No.33        1 = 1/2 + 1/3 + 1/8 + 1/60 + 1/65 + 1/104
  34. No.34        1 = 1/2 + 1/3 + 1/8 + 1/60 + 1/72 + 1/90
  35. No.35        1 = 1/2 + 1/3 + 1/8 + 1/63 + 1/72 + 1/84
  36. No.36        1 = 1/2 + 1/3 + 1/9 + 1/24 + 1/136 + 1/153
  37. No.37        1 = 1/2 + 1/3 + 1/9 + 1/26 + 1/99 + 1/143
  38. No.38        1 = 1/2 + 1/3 + 1/9 + 1/27 + 1/81 + 1/162
  39. No.39        1 = 1/2 + 1/3 + 1/9 + 1/27 + 1/90 + 1/135
  40. No.40        1 = 1/2 + 1/3 + 1/9 + 1/28 + 1/84 + 1/126
  41. No.41        1 = 1/2 + 1/3 + 1/9 + 1/30 + 1/70 + 1/126
  42. No.42        1 = 1/2 + 1/3 + 1/9 + 1/30 + 1/72 + 1/120
  43. No.43        1 = 1/2 + 1/3 + 1/9 + 1/32 + 1/72 + 1/96
  44. No.44        1 = 1/2 + 1/3 + 1/9 + 1/33 + 1/66 + 1/99
  45. No.45        1 = 1/2 + 1/3 + 1/9 + 1/33 + 1/72 + 1/88
  46. No.46        1 = 1/2 + 1/3 + 1/9 + 1/34 + 1/51 + 1/153
  47. No.47        1 = 1/2 + 1/3 + 1/9 + 1/35 + 1/63 + 1/90
  48. No.48        1 = 1/2 + 1/3 + 1/9 + 1/36 + 1/48 + 1/144
  49. No.49        1 = 1/2 + 1/3 + 1/9 + 1/36 + 1/52 + 1/117
  50. No.50        1 = 1/2 + 1/3 + 1/9 + 1/36 + 1/54 + 1/108
  51. No.51        1 = 1/2 + 1/3 + 1/9 + 1/36 + 1/60 + 1/90
  52. No.52        1 = 1/2 + 1/3 + 1/9 + 1/36 + 1/63 + 1/84
  53. No.53        1 = 1/2 + 1/3 + 1/9 + 1/39 + 1/45 + 1/130
  54. No.54        1 = 1/2 + 1/3 + 1/9 + 1/40 + 1/45 + 1/120
  55. No.55        1 = 1/2 + 1/3 + 1/9 + 1/40 + 1/60 + 1/72
  56. No.56        1 = 1/2 + 1/3 + 1/9 + 1/42 + 1/45 + 1/105
  57. No.57        1 = 1/2 + 1/3 + 1/9 + 1/42 + 1/56 + 1/72
  58. No.58        1 = 1/2 + 1/3 + 1/9 + 1/45 + 1/48 + 1/80
  59. No.59        1 = 1/2 + 1/3 + 1/9 + 1/45 + 1/50 + 1/75
  60. No.60        1 = 1/2 + 1/3 + 1/9 + 1/45 + 1/55 + 1/66
  61. No.61        1 = 1/2 + 1/3 + 1/10 + 1/20 + 1/96 + 1/160
  62. No.62        1 = 1/2 + 1/3 + 1/10 + 1/20 + 1/100 + 1/150
  63. No.63        1 = 1/2 + 1/3 + 1/10 + 1/20 + 1/105 + 1/140
  64. No.64        1 = 1/2 + 1/3 + 1/10 + 1/20 + 1/108 + 1/135
  65. No.65        1 = 1/2 + 1/3 + 1/10 + 1/20 + 1/110 + 1/132
  66. No.66        1 = 1/2 + 1/3 + 1/10 + 1/21 + 1/84 + 1/140
  67. No.67        1 = 1/2 + 1/3 + 1/10 + 1/21 + 1/90 + 1/126
  68. No.68        1 = 1/2 + 1/3 + 1/10 + 1/22 + 1/90 + 1/99
  69. No.69        1 = 1/2 + 1/3 + 1/10 + 1/23 + 1/69 + 1/115
  70. No.70        1 = 1/2 + 1/3 + 1/10 + 1/24 + 1/56 + 1/140
  71. No.71        1 = 1/2 + 1/3 + 1/10 + 1/24 + 1/60 + 1/120
  72. No.72        1 = 1/2 + 1/3 + 1/10 + 1/24 + 1/65 + 1/104
  73. No.73        1 = 1/2 + 1/3 + 1/10 + 1/24 + 1/72 + 1/90
  74. No.74        1 = 1/2 + 1/3 + 1/10 + 1/25 + 1/50 + 1/150
  75. No.75        1 = 1/2 + 1/3 + 1/10 + 1/25 + 1/60 + 1/100
  76. No.76        1 = 1/2 + 1/3 + 1/10 + 1/26 + 1/65 + 1/78
  77. No.77        1 = 1/2 + 1/3 + 1/10 + 1/27 + 1/45 + 1/135
  78. No.78        1 = 1/2 + 1/3 + 1/10 + 1/27 + 1/54 + 1/90
  79. No.79        1 = 1/2 + 1/3 + 1/10 + 1/28 + 1/42 + 1/140
  80. No.80        1 = 1/2 + 1/3 + 1/10 + 1/28 + 1/60 + 1/70
  81. No.81        1 = 1/2 + 1/3 + 1/10 + 1/30 + 1/39 + 1/130
  82. No.82        1 = 1/2 + 1/3 + 1/10 + 1/30 + 1/40 + 1/120
  83. No.83        1 = 1/2 + 1/3 + 1/10 + 1/30 + 1/42 + 1/105
  84. No.84        1 = 1/2 + 1/3 + 1/10 + 1/30 + 1/45 + 1/90
  85. No.85        1 = 1/2 + 1/3 + 1/10 + 1/30 + 1/48 + 1/80
  86. No.86        1 = 1/2 + 1/3 + 1/10 + 1/30 + 1/50 + 1/75
  87. No.87        1 = 1/2 + 1/3 + 1/10 + 1/30 + 1/55 + 1/66
  88. No.88        1 = 1/2 + 1/3 + 1/10 + 1/32 + 1/40 + 1/96
  89. No.89        1 = 1/2 + 1/3 + 1/10 + 1/33 + 1/40 + 1/88
  90. No.90        1 = 1/2 + 1/3 + 1/10 + 1/35 + 1/42 + 1/70
  91. No.91        1 = 1/2 + 1/3 + 1/10 + 1/35 + 1/45 + 1/63
  92. No.92        1 = 1/2 + 1/3 + 1/10 + 1/36 + 1/40 + 1/72
  93. No.93        1 = 1/2 + 1/3 + 1/10 + 1/36 + 1/45 + 1/60
  94. No.94        1 = 1/2 + 1/3 + 1/10 + 1/40 + 1/42 + 1/56
  95. No.95        1 = 1/2 + 1/3 + 1/11 + 1/18 + 1/90 + 1/110
  96. No.96        1 = 1/2 + 1/3 + 1/11 + 1/20 + 1/55 + 1/132
  97. No.97        1 = 1/2 + 1/3 + 1/11 + 1/20 + 1/60 + 1/110
  98. No.98        1 = 1/2 + 1/3 + 1/11 + 1/21 + 1/66 + 1/77
  99. No.99        1 = 1/2 + 1/3 + 1/11 + 1/22 + 1/42 + 1/154
  100. No.100        1 = 1/2 + 1/3 + 1/11 + 1/22 + 1/44 + 1/132
  101. No.101        1 = 1/2 + 1/3 + 1/11 + 1/24 + 1/40 + 1/110
  102. No.102        1 = 1/2 + 1/3 + 1/11 + 1/24 + 1/44 + 1/88
  103. No.103        1 = 1/2 + 1/3 + 1/11 + 1/26 + 1/33 + 1/143
  104. No.104        1 = 1/2 + 1/3 + 1/12 + 1/15 + 1/96 + 1/160
  105. No.105        1 = 1/2 + 1/3 + 1/12 + 1/15 + 1/100 + 1/150
  106. No.106        1 = 1/2 + 1/3 + 1/12 + 1/15 + 1/105 + 1/140
  107. No.107        1 = 1/2 + 1/3 + 1/12 + 1/15 + 1/108 + 1/135
  108. No.108        1 = 1/2 + 1/3 + 1/12 + 1/15 + 1/110 + 1/132
  109. No.109        1 = 1/2 + 1/3 + 1/12 + 1/16 + 1/72 + 1/144
  110. No.110        1 = 1/2 + 1/3 + 1/12 + 1/16 + 1/80 + 1/120
  111. No.111        1 = 1/2 + 1/3 + 1/12 + 1/16 + 1/84 + 1/112
  112. No.112        1 = 1/2 + 1/3 + 1/12 + 1/17 + 1/68 + 1/102
  113. No.113        1 = 1/2 + 1/3 + 1/12 + 1/18 + 1/48 + 1/144
  114. No.114        1 = 1/2 + 1/3 + 1/12 + 1/18 + 1/52 + 1/117
  115. No.115        1 = 1/2 + 1/3 + 1/12 + 1/18 + 1/54 + 1/108
  116. No.116        1 = 1/2 + 1/3 + 1/12 + 1/18 + 1/60 + 1/90
  117. No.117        1 = 1/2 + 1/3 + 1/12 + 1/18 + 1/63 + 1/84
  118. No.118        1 = 1/2 + 1/3 + 1/12 + 1/19 + 1/57 + 1/76
  119. No.119        1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/39 + 1/130
  120. No.120        1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/40 + 1/120
  121. No.121        1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/42 + 1/105
  122. No.122        1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/45 + 1/90
  123. No.123        1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/48 + 1/80
  124. No.124        1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/50 + 1/75
  125. No.125        1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/55 + 1/66
  126. No.126        1 = 1/2 + 1/3 + 1/12 + 1/21 + 1/35 + 1/140
  127. No.127        1 = 1/2 + 1/3 + 1/12 + 1/21 + 1/36 + 1/126
  128. No.128        1 = 1/2 + 1/3 + 1/12 + 1/21 + 1/42 + 1/84
  129. No.129        1 = 1/2 + 1/3 + 1/12 + 1/21 + 1/44 + 1/77
  130. No.130        1 = 1/2 + 1/3 + 1/12 + 1/22 + 1/33 + 1/132
  131. No.131        1 = 1/2 + 1/3 + 1/12 + 1/22 + 1/36 + 1/99
  132. No.132        1 = 1/2 + 1/3 + 1/12 + 1/22 + 1/44 + 1/66
  133. No.133        1 = 1/2 + 1/3 + 1/12 + 1/24 + 1/30 + 1/120
  134. No.134        1 = 1/2 + 1/3 + 1/12 + 1/24 + 1/32 + 1/96
  135. No.135        1 = 1/2 + 1/3 + 1/12 + 1/24 + 1/33 + 1/88
  136. No.136        1 = 1/2 + 1/3 + 1/12 + 1/24 + 1/36 + 1/72
  137. No.137        1 = 1/2 + 1/3 + 1/12 + 1/24 + 1/40 + 1/60
  138. No.138        1 = 1/2 + 1/3 + 1/12 + 1/24 + 1/42 + 1/56
  139. No.139        1 = 1/2 + 1/3 + 1/12 + 1/25 + 1/30 + 1/100
  140. No.140        1 = 1/2 + 1/3 + 1/12 + 1/26 + 1/39 + 1/52
  141. No.141        1 = 1/2 + 1/3 + 1/12 + 1/27 + 1/36 + 1/54
  142. No.142        1 = 1/2 + 1/3 + 1/12 + 1/28 + 1/30 + 1/70
  143. No.143        1 = 1/2 + 1/3 + 1/12 + 1/30 + 1/36 + 1/45
  144. No.144        1 = 1/2 + 1/3 + 1/13 + 1/14 + 1/84 + 1/156
  145. No.145        1 = 1/2 + 1/3 + 1/13 + 1/15 + 1/60 + 1/156
  146. No.146        1 = 1/2 + 1/3 + 1/13 + 1/15 + 1/65 + 1/130
  147. No.147        1 = 1/2 + 1/3 + 1/13 + 1/16 + 1/48 + 1/156
  148. No.148        1 = 1/2 + 1/3 + 1/13 + 1/18 + 1/36 + 1/156
  149. No.149        1 = 1/2 + 1/3 + 1/13 + 1/18 + 1/39 + 1/117
  150. No.150        1 = 1/2 + 1/3 + 1/13 + 1/20 + 1/30 + 1/156
  151. No.151        1 = 1/2 + 1/3 + 1/13 + 1/21 + 1/28 + 1/156
  152. No.152        1 = 1/2 + 1/3 + 1/13 + 1/24 + 1/26 + 1/104
  153. No.153        1 = 1/2 + 1/3 + 1/14 + 1/15 + 1/60 + 1/84
  154. No.154        1 = 1/2 + 1/3 + 1/14 + 1/16 + 1/42 + 1/112
  155. No.155        1 = 1/2 + 1/3 + 1/14 + 1/16 + 1/48 + 1/84
  156. No.156        1 = 1/2 + 1/3 + 1/14 + 1/18 + 1/35 + 1/90
  157. No.157        1 = 1/2 + 1/3 + 1/14 + 1/18 + 1/36 + 1/84
  158. No.158        1 = 1/2 + 1/3 + 1/14 + 1/18 + 1/42 + 1/63
  159. No.159        1 = 1/2 + 1/3 + 1/14 + 1/20 + 1/28 + 1/105
  160. No.160        1 = 1/2 + 1/3 + 1/14 + 1/20 + 1/30 + 1/84
  161. No.161        1 = 1/2 + 1/3 + 1/14 + 1/20 + 1/35 + 1/60
  162. No.162        1 = 1/2 + 1/3 + 1/14 + 1/21 + 1/28 + 1/84
  163. No.163        1 = 1/2 + 1/3 + 1/14 + 1/21 + 1/30 + 1/70
  164. No.164        1 = 1/2 + 1/3 + 1/14 + 1/24 + 1/28 + 1/56
  165. No.165        1 = 1/2 + 1/3 + 1/14 + 1/24 + 1/35 + 1/40
  166. No.166        1 = 1/2 + 1/3 + 1/15 + 1/16 + 1/32 + 1/160
  167. No.167        1 = 1/2 + 1/3 + 1/15 + 1/16 + 1/35 + 1/112
  168. No.168        1 = 1/2 + 1/3 + 1/15 + 1/16 + 1/40 + 1/80
  169. No.169        1 = 1/2 + 1/3 + 1/15 + 1/16 + 1/48 + 1/60
  170. No.170        1 = 1/2 + 1/3 + 1/15 + 1/17 + 1/34 + 1/85
  171. No.171        1 = 1/2 + 1/3 + 1/15 + 1/18 + 1/27 + 1/135
  172. No.172        1 = 1/2 + 1/3 + 1/15 + 1/18 + 1/30 + 1/90
  173. No.173        1 = 1/2 + 1/3 + 1/15 + 1/18 + 1/35 + 1/63
  174. No.174        1 = 1/2 + 1/3 + 1/15 + 1/18 + 1/36 + 1/60
  175. No.175        1 = 1/2 + 1/3 + 1/15 + 1/20 + 1/24 + 1/120
  176. No.176        1 = 1/2 + 1/3 + 1/15 + 1/20 + 1/25 + 1/100
  177. No.177        1 = 1/2 + 1/3 + 1/15 + 1/20 + 1/28 + 1/70
  178. No.178        1 = 1/2 + 1/3 + 1/15 + 1/20 + 1/30 + 1/60
  179. No.179        1 = 1/2 + 1/3 + 1/15 + 1/20 + 1/36 + 1/45
  180. No.180        1 = 1/2 + 1/3 + 1/15 + 1/21 + 1/28 + 1/60
  181. No.181        1 = 1/2 + 1/3 + 1/15 + 1/21 + 1/35 + 1/42
  182. No.182        1 = 1/2 + 1/3 + 1/15 + 1/24 + 1/30 + 1/40
  183. No.183        1 = 1/2 + 1/3 + 1/16 + 1/18 + 1/24 + 1/144
  184. No.184        1 = 1/2 + 1/3 + 1/16 + 1/18 + 1/36 + 1/48
  185. No.185        1 = 1/2 + 1/3 + 1/16 + 1/20 + 1/24 + 1/80
  186. No.186        1 = 1/2 + 1/3 + 1/16 + 1/20 + 1/30 + 1/48
  187. No.187        1 = 1/2 + 1/3 + 1/16 + 1/21 + 1/28 + 1/48
  188. No.188        1 = 1/2 + 1/3 + 1/18 + 1/20 + 1/30 + 1/36
  189. No.189        1 = 1/2 + 1/3 + 1/18 + 1/21 + 1/28 + 1/36
  190. No.190        1 = 1/2 + 1/3 + 1/20 + 1/21 + 1/28 + 1/30
  191. No.191        1 = 1/2 + 1/4 + 1/5 + 1/29 + 1/116 + 1/145
  192. No.192        1 = 1/2 + 1/4 + 1/5 + 1/30 + 1/96 + 1/160
  193. No.193        1 = 1/2 + 1/4 + 1/5 + 1/30 + 1/100 + 1/150
  194. No.194        1 = 1/2 + 1/4 + 1/5 + 1/30 + 1/105 + 1/140
  195. No.195        1 = 1/2 + 1/4 + 1/5 + 1/30 + 1/108 + 1/135
  196. No.196        1 = 1/2 + 1/4 + 1/5 + 1/30 + 1/110 + 1/132
  197. No.197        1 = 1/2 + 1/4 + 1/5 + 1/32 + 1/80 + 1/160
  198. No.198        1 = 1/2 + 1/4 + 1/5 + 1/32 + 1/96 + 1/120
  199. No.199        1 = 1/2 + 1/4 + 1/5 + 1/33 + 1/88 + 1/120
  200. No.200        1 = 1/2 + 1/4 + 1/5 + 1/35 + 1/70 + 1/140
  201. No.201        1 = 1/2 + 1/4 + 1/5 + 1/35 + 1/80 + 1/112
  202. No.202        1 = 1/2 + 1/4 + 1/5 + 1/35 + 1/84 + 1/105
  203. No.203        1 = 1/2 + 1/4 + 1/5 + 1/36 + 1/70 + 1/126
  204. No.204        1 = 1/2 + 1/4 + 1/5 + 1/36 + 1/72 + 1/120
  205. No.205        1 = 1/2 + 1/4 + 1/5 + 1/38 + 1/76 + 1/95
  206. No.206        1 = 1/2 + 1/4 + 1/5 + 1/39 + 1/60 + 1/130
  207. No.207        1 = 1/2 + 1/4 + 1/5 + 1/40 + 1/56 + 1/140
  208. No.208        1 = 1/2 + 1/4 + 1/5 + 1/40 + 1/60 + 1/120
  209. No.209        1 = 1/2 + 1/4 + 1/5 + 1/40 + 1/65 + 1/104
  210. No.210        1 = 1/2 + 1/4 + 1/5 + 1/40 + 1/72 + 1/90
  211. No.211        1 = 1/2 + 1/4 + 1/5 + 1/42 + 1/56 + 1/120
  212. No.212        1 = 1/2 + 1/4 + 1/5 + 1/42 + 1/60 + 1/105
  213. No.213        1 = 1/2 + 1/4 + 1/5 + 1/42 + 1/70 + 1/84
  214. No.214        1 = 1/2 + 1/4 + 1/5 + 1/44 + 1/55 + 1/110
  215. No.215        1 = 1/2 + 1/4 + 1/5 + 1/44 + 1/70 + 1/77
  216. No.216        1 = 1/2 + 1/4 + 1/5 + 1/45 + 1/48 + 1/144
  217. No.217        1 = 1/2 + 1/4 + 1/5 + 1/45 + 1/52 + 1/117
  218. No.218        1 = 1/2 + 1/4 + 1/5 + 1/45 + 1/54 + 1/108
  219. No.219        1 = 1/2 + 1/4 + 1/5 + 1/45 + 1/60 + 1/90
  220. No.220        1 = 1/2 + 1/4 + 1/5 + 1/45 + 1/63 + 1/84
  221. No.221        1 = 1/2 + 1/4 + 1/5 + 1/48 + 1/60 + 1/80
  222. No.222        1 = 1/2 + 1/4 + 1/5 + 1/50 + 1/60 + 1/75
  223. No.223        1 = 1/2 + 1/4 + 1/5 + 1/55 + 1/60 + 1/66
  224. No.224        1 = 1/2 + 1/4 + 1/6 + 1/15 + 1/96 + 1/160
  225. No.225        1 = 1/2 + 1/4 + 1/6 + 1/15 + 1/100 + 1/150
  226. No.226        1 = 1/2 + 1/4 + 1/6 + 1/15 + 1/105 + 1/140
  227. No.227        1 = 1/2 + 1/4 + 1/6 + 1/15 + 1/108 + 1/135
  228. No.228        1 = 1/2 + 1/4 + 1/6 + 1/15 + 1/110 + 1/132
  229. No.229        1 = 1/2 + 1/4 + 1/6 + 1/16 + 1/72 + 1/144
  230. No.230        1 = 1/2 + 1/4 + 1/6 + 1/16 + 1/80 + 1/120
  231. No.231        1 = 1/2 + 1/4 + 1/6 + 1/16 + 1/84 + 1/112
  232. No.232        1 = 1/2 + 1/4 + 1/6 + 1/17 + 1/68 + 1/102
  233. No.233        1 = 1/2 + 1/4 + 1/6 + 1/18 + 1/48 + 1/144
  234. No.234        1 = 1/2 + 1/4 + 1/6 + 1/18 + 1/52 + 1/117
  235. No.235        1 = 1/2 + 1/4 + 1/6 + 1/18 + 1/54 + 1/108
  236. No.236        1 = 1/2 + 1/4 + 1/6 + 1/18 + 1/60 + 1/90
  237. No.237        1 = 1/2 + 1/4 + 1/6 + 1/18 + 1/63 + 1/84
  238. No.238        1 = 1/2 + 1/4 + 1/6 + 1/19 + 1/57 + 1/76
  239. No.239        1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/39 + 1/130
  240. No.240        1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/40 + 1/120
  241. No.241        1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/42 + 1/105
  242. No.242        1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/45 + 1/90
  243. No.243        1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/48 + 1/80
  244. No.244        1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/50 + 1/75
  245. No.245        1 = 1/2 + 1/4 + 1/6 + 1/20 + 1/55 + 1/66
  246. No.246        1 = 1/2 + 1/4 + 1/6 + 1/21 + 1/35 + 1/140
  247. No.247        1 = 1/2 + 1/4 + 1/6 + 1/21 + 1/36 + 1/126
  248. No.248        1 = 1/2 + 1/4 + 1/6 + 1/21 + 1/42 + 1/84
  249. No.249        1 = 1/2 + 1/4 + 1/6 + 1/21 + 1/44 + 1/77
  250. No.250        1 = 1/2 + 1/4 + 1/6 + 1/22 + 1/33 + 1/132
  251. No.251        1 = 1/2 + 1/4 + 1/6 + 1/22 + 1/36 + 1/99
  252. No.252        1 = 1/2 + 1/4 + 1/6 + 1/22 + 1/44 + 1/66
  253. No.253        1 = 1/2 + 1/4 + 1/6 + 1/24 + 1/30 + 1/120
  254. No.254        1 = 1/2 + 1/4 + 1/6 + 1/24 + 1/32 + 1/96
  255. No.255        1 = 1/2 + 1/4 + 1/6 + 1/24 + 1/33 + 1/88
  256. No.256        1 = 1/2 + 1/4 + 1/6 + 1/24 + 1/36 + 1/72
  257. No.257        1 = 1/2 + 1/4 + 1/6 + 1/24 + 1/40 + 1/60
  258. No.258        1 = 1/2 + 1/4 + 1/6 + 1/24 + 1/42 + 1/56
  259. No.259        1 = 1/2 + 1/4 + 1/6 + 1/25 + 1/30 + 1/100
  260. No.260        1 = 1/2 + 1/4 + 1/6 + 1/26 + 1/39 + 1/52
  261. No.261        1 = 1/2 + 1/4 + 1/6 + 1/27 + 1/36 + 1/54
  262. No.262        1 = 1/2 + 1/4 + 1/6 + 1/28 + 1/30 + 1/70
  263. No.263        1 = 1/2 + 1/4 + 1/6 + 1/30 + 1/36 + 1/45
  264. No.264        1 = 1/2 + 1/4 + 1/7 + 1/11 + 1/110 + 1/140
  265. No.265        1 = 1/2 + 1/4 + 1/7 + 1/12 + 1/60 + 1/140
  266. No.266        1 = 1/2 + 1/4 + 1/7 + 1/12 + 1/63 + 1/126
  267. No.267        1 = 1/2 + 1/4 + 1/7 + 1/12 + 1/70 + 1/105
  268. No.268        1 = 1/2 + 1/4 + 1/7 + 1/12 + 1/78 + 1/91
  269. No.269        1 = 1/2 + 1/4 + 1/7 + 1/13 + 1/42 + 1/156
  270. No.270        1 = 1/2 + 1/4 + 1/7 + 1/13 + 1/52 + 1/91
  271. No.271        1 = 1/2 + 1/4 + 1/7 + 1/14 + 1/35 + 1/140
  272. No.272        1 = 1/2 + 1/4 + 1/7 + 1/14 + 1/36 + 1/126
  273. No.273        1 = 1/2 + 1/4 + 1/7 + 1/14 + 1/42 + 1/84
  274. No.274        1 = 1/2 + 1/4 + 1/7 + 1/14 + 1/44 + 1/77
  275. No.275        1 = 1/2 + 1/4 + 1/7 + 1/15 + 1/30 + 1/140
  276. No.276        1 = 1/2 + 1/4 + 1/7 + 1/15 + 1/35 + 1/84
  277. No.277        1 = 1/2 + 1/4 + 1/7 + 1/15 + 1/42 + 1/60
  278. No.278        1 = 1/2 + 1/4 + 1/7 + 1/16 + 1/28 + 1/112
  279. No.279        1 = 1/2 + 1/4 + 1/7 + 1/16 + 1/42 + 1/48
  280. No.280        1 = 1/2 + 1/4 + 1/7 + 1/18 + 1/28 + 1/63
  281. No.281        1 = 1/2 + 1/4 + 1/7 + 1/18 + 1/36 + 1/42
  282. No.282        1 = 1/2 + 1/4 + 1/7 + 1/20 + 1/21 + 1/105
  283. No.283        1 = 1/2 + 1/4 + 1/7 + 1/20 + 1/30 + 1/42
  284. No.284        1 = 1/2 + 1/4 + 1/7 + 1/21 + 1/24 + 1/56
  285. No.285        1 = 1/2 + 1/4 + 1/7 + 1/21 + 1/28 + 1/42
  286. No.286        1 = 1/2 + 1/4 + 1/8 + 1/9 + 1/136 + 1/153
  287. No.287        1 = 1/2 + 1/4 + 1/8 + 1/10 + 1/56 + 1/140
  288. No.288        1 = 1/2 + 1/4 + 1/8 + 1/10 + 1/60 + 1/120
  289. No.289        1 = 1/2 + 1/4 + 1/8 + 1/10 + 1/65 + 1/104
  290. No.290        1 = 1/2 + 1/4 + 1/8 + 1/10 + 1/72 + 1/90
  291. No.291        1 = 1/2 + 1/4 + 1/8 + 1/11 + 1/40 + 1/110
  292. No.292        1 = 1/2 + 1/4 + 1/8 + 1/11 + 1/44 + 1/88
  293. No.293        1 = 1/2 + 1/4 + 1/8 + 1/12 + 1/30 + 1/120
  294. No.294        1 = 1/2 + 1/4 + 1/8 + 1/12 + 1/32 + 1/96
  295. No.295        1 = 1/2 + 1/4 + 1/8 + 1/12 + 1/33 + 1/88
  296. No.296        1 = 1/2 + 1/4 + 1/8 + 1/12 + 1/36 + 1/72
  297. No.297        1 = 1/2 + 1/4 + 1/8 + 1/12 + 1/40 + 1/60
  298. No.298        1 = 1/2 + 1/4 + 1/8 + 1/12 + 1/42 + 1/56
  299. No.299        1 = 1/2 + 1/4 + 1/8 + 1/13 + 1/24 + 1/156
  300. No.300        1 = 1/2 + 1/4 + 1/8 + 1/13 + 1/26 + 1/104
  301. No.301        1 = 1/2 + 1/4 + 1/8 + 1/14 + 1/24 + 1/84
  302. No.302        1 = 1/2 + 1/4 + 1/8 + 1/14 + 1/28 + 1/56
  303. No.303        1 = 1/2 + 1/4 + 1/8 + 1/14 + 1/35 + 1/40
  304. No.304        1 = 1/2 + 1/4 + 1/8 + 1/15 + 1/20 + 1/120
  305. No.305        1 = 1/2 + 1/4 + 1/8 + 1/15 + 1/24 + 1/60
  306. No.306        1 = 1/2 + 1/4 + 1/8 + 1/15 + 1/30 + 1/40
  307. No.307        1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/18 + 1/144
  308. No.308        1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/20 + 1/80
  309. No.309        1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/24 + 1/48
  310. No.310        1 = 1/2 + 1/4 + 1/8 + 1/18 + 1/24 + 1/36
  311. No.311        1 = 1/2 + 1/4 + 1/8 + 1/20 + 1/24 + 1/30
  312. No.312        1 = 1/2 + 1/4 + 1/8 + 1/21 + 1/24 + 1/28
  313. No.313        1 = 1/2 + 1/4 + 1/9 + 1/10 + 1/36 + 1/90
  314. No.314        1 = 1/2 + 1/4 + 1/9 + 1/10 + 1/40 + 1/72
  315. No.315        1 = 1/2 + 1/4 + 1/9 + 1/10 + 1/45 + 1/60
  316. No.316        1 = 1/2 + 1/4 + 1/9 + 1/12 + 1/21 + 1/126
  317. No.317        1 = 1/2 + 1/4 + 1/9 + 1/12 + 1/22 + 1/99
  318. No.318        1 = 1/2 + 1/4 + 1/9 + 1/12 + 1/24 + 1/72
  319. No.319        1 = 1/2 + 1/4 + 1/9 + 1/12 + 1/27 + 1/54
  320. No.320        1 = 1/2 + 1/4 + 1/9 + 1/12 + 1/30 + 1/45
  321. No.321        1 = 1/2 + 1/4 + 1/9 + 1/13 + 1/18 + 1/156
  322. No.322        1 = 1/2 + 1/4 + 1/9 + 1/14 + 1/18 + 1/84
  323. No.323        1 = 1/2 + 1/4 + 1/9 + 1/15 + 1/18 + 1/60
  324. No.324        1 = 1/2 + 1/4 + 1/9 + 1/15 + 1/20 + 1/45
  325. No.325        1 = 1/2 + 1/4 + 1/9 + 1/16 + 1/18 + 1/48
  326. No.326        1 = 1/2 + 1/4 + 1/9 + 1/18 + 1/20 + 1/30
  327. No.327        1 = 1/2 + 1/4 + 1/9 + 1/18 + 1/21 + 1/28
  328. No.328        1 = 1/2 + 1/4 + 1/10 + 1/11 + 1/20 + 1/110
  329. No.329        1 = 1/2 + 1/4 + 1/10 + 1/12 + 1/18 + 1/90
  330. No.330        1 = 1/2 + 1/4 + 1/10 + 1/12 + 1/20 + 1/60
  331. No.331        1 = 1/2 + 1/4 + 1/10 + 1/12 + 1/24 + 1/40
  332. No.332        1 = 1/2 + 1/4 + 1/10 + 1/13 + 1/15 + 1/156
  333. No.333        1 = 1/2 + 1/4 + 1/10 + 1/14 + 1/15 + 1/84
  334. No.334        1 = 1/2 + 1/4 + 1/10 + 1/14 + 1/20 + 1/35
  335. No.335        1 = 1/2 + 1/4 + 1/10 + 1/15 + 1/16 + 1/48
  336. No.336        1 = 1/2 + 1/4 + 1/10 + 1/15 + 1/18 + 1/36
  337. No.337        1 = 1/2 + 1/4 + 1/10 + 1/15 + 1/20 + 1/30
  338. No.338        1 = 1/2 + 1/4 + 1/10 + 1/15 + 1/21 + 1/28
  339. No.339        1 = 1/2 + 1/4 + 1/11 + 1/12 + 1/15 + 1/110
  340. No.340        1 = 1/2 + 1/4 + 1/11 + 1/12 + 1/22 + 1/33
  341. No.341        1 = 1/2 + 1/4 + 1/12 + 1/14 + 1/15 + 1/35
  342. No.342        1 = 1/2 + 1/5 + 1/6 + 1/9 + 1/70 + 1/126
  343. No.343        1 = 1/2 + 1/5 + 1/6 + 1/9 + 1/72 + 1/120
  344. No.344        1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/39 + 1/130
  345. No.345        1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/40 + 1/120
  346. No.346        1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/42 + 1/105
  347. No.347        1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/45 + 1/90
  348. No.348        1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/48 + 1/80
  349. No.349        1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/50 + 1/75
  350. No.350        1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/55 + 1/66
  351. No.351        1 = 1/2 + 1/5 + 1/6 + 1/11 + 1/30 + 1/110
  352. No.352        1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/24 + 1/120
  353. No.353        1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/25 + 1/100
  354. No.354        1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/28 + 1/70
  355. No.355        1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/30 + 1/60
  356. No.356        1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/36 + 1/45
  357. No.357        1 = 1/2 + 1/5 + 1/6 + 1/13 + 1/20 + 1/156
  358. No.358        1 = 1/2 + 1/5 + 1/6 + 1/14 + 1/20 + 1/84
  359. No.359        1 = 1/2 + 1/5 + 1/6 + 1/14 + 1/21 + 1/70
  360. No.360        1 = 1/2 + 1/5 + 1/6 + 1/14 + 1/30 + 1/35
  361. No.361        1 = 1/2 + 1/5 + 1/6 + 1/15 + 1/18 + 1/90
  362. No.362        1 = 1/2 + 1/5 + 1/6 + 1/15 + 1/20 + 1/60
  363. No.363        1 = 1/2 + 1/5 + 1/6 + 1/15 + 1/24 + 1/40
  364. No.364        1 = 1/2 + 1/5 + 1/6 + 1/16 + 1/20 + 1/48
  365. No.365        1 = 1/2 + 1/5 + 1/6 + 1/18 + 1/20 + 1/36
  366. No.366        1 = 1/2 + 1/5 + 1/6 + 1/20 + 1/21 + 1/28
  367. No.367        1 = 1/2 + 1/5 + 1/7 + 1/8 + 1/40 + 1/140
  368. No.368        1 = 1/2 + 1/5 + 1/7 + 1/8 + 1/42 + 1/120
  369. No.369        1 = 1/2 + 1/5 + 1/7 + 1/8 + 1/56 + 1/70
  370. No.370        1 = 1/2 + 1/5 + 1/7 + 1/9 + 1/42 + 1/45
  371. No.371        1 = 1/2 + 1/5 + 1/7 + 1/10 + 1/20 + 1/140
  372. No.372        1 = 1/2 + 1/5 + 1/7 + 1/10 + 1/21 + 1/105
  373. No.373        1 = 1/2 + 1/5 + 1/7 + 1/10 + 1/30 + 1/42
  374. No.374        1 = 1/2 + 1/5 + 1/7 + 1/12 + 1/15 + 1/140
  375. No.375        1 = 1/2 + 1/5 + 1/7 + 1/12 + 1/20 + 1/42
  376. No.376        1 = 1/2 + 1/5 + 1/7 + 1/14 + 1/20 + 1/28
  377. No.377        1 = 1/2 + 1/5 + 1/8 + 1/9 + 1/18 + 1/120
  378. No.378        1 = 1/2 + 1/5 + 1/8 + 1/9 + 1/20 + 1/72
  379. No.379        1 = 1/2 + 1/5 + 1/8 + 1/9 + 1/24 + 1/45
  380. No.380        1 = 1/2 + 1/5 + 1/8 + 1/10 + 1/15 + 1/120
  381. No.381        1 = 1/2 + 1/5 + 1/8 + 1/10 + 1/16 + 1/80
  382. No.382        1 = 1/2 + 1/5 + 1/8 + 1/10 + 1/20 + 1/40
  383. No.383        1 = 1/2 + 1/5 + 1/8 + 1/10 + 1/24 + 1/30
  384. No.384        1 = 1/2 + 1/5 + 1/8 + 1/12 + 1/15 + 1/40
  385. No.385        1 = 1/2 + 1/5 + 1/8 + 1/12 + 1/20 + 1/24
  386. No.386        1 = 1/2 + 1/5 + 1/9 + 1/10 + 1/15 + 1/45
  387. No.387        1 = 1/2 + 1/5 + 1/9 + 1/10 + 1/18 + 1/30
  388. No.388        1 = 1/2 + 1/5 + 1/9 + 1/12 + 1/18 + 1/20
  389. No.389        1 = 1/2 + 1/5 + 1/10 + 1/12 + 1/15 + 1/20
  390. No.390        1 = 1/2 + 1/6 + 1/7 + 1/8 + 1/21 + 1/56
  391. No.391        1 = 1/2 + 1/6 + 1/7 + 1/8 + 1/24 + 1/42
  392. No.392        1 = 1/2 + 1/6 + 1/7 + 1/9 + 1/14 + 1/126
  393. No.393        1 = 1/2 + 1/6 + 1/7 + 1/9 + 1/18 + 1/42
  394. No.394        1 = 1/2 + 1/6 + 1/7 + 1/10 + 1/12 + 1/140
  395. No.395        1 = 1/2 + 1/6 + 1/7 + 1/10 + 1/15 + 1/42
  396. No.396        1 = 1/2 + 1/6 + 1/7 + 1/12 + 1/14 + 1/28
  397. No.397        1 = 1/2 + 1/6 + 1/8 + 1/9 + 1/12 + 1/72
  398. No.398        1 = 1/2 + 1/6 + 1/8 + 1/9 + 1/18 + 1/24
  399. No.399        1 = 1/2 + 1/6 + 1/8 + 1/10 + 1/12 + 1/40
  400. No.400        1 = 1/2 + 1/6 + 1/8 + 1/10 + 1/15 + 1/24
  401. No.401        1 = 1/2 + 1/6 + 1/9 + 1/10 + 1/15 + 1/18
  402. No.402        1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/24 + 1/120
  403. No.403        1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/25 + 1/100
  404. No.404        1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/28 + 1/70
  405. No.405        1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/30 + 1/60
  406. No.406        1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/36 + 1/45
  407. No.407        1 = 1/3 + 1/4 + 1/5 + 1/7 + 1/15 + 1/140
  408. No.408        1 = 1/3 + 1/4 + 1/5 + 1/7 + 1/20 + 1/42
  409. No.409        1 = 1/3 + 1/4 + 1/5 + 1/8 + 1/12 + 1/120
  410. No.410        1 = 1/3 + 1/4 + 1/5 + 1/8 + 1/15 + 1/40
  411. No.411        1 = 1/3 + 1/4 + 1/5 + 1/8 + 1/20 + 1/24
  412. No.412        1 = 1/3 + 1/4 + 1/5 + 1/9 + 1/12 + 1/45
  413. No.413        1 = 1/3 + 1/4 + 1/5 + 1/9 + 1/18 + 1/20
  414. No.414        1 = 1/3 + 1/4 + 1/5 + 1/10 + 1/12 + 1/30
  415. No.415        1 = 1/3 + 1/4 + 1/5 + 1/10 + 1/15 + 1/20
  416. No.416        1 = 1/3 + 1/4 + 1/6 + 1/7 + 1/10 + 1/140
  417. No.417        1 = 1/3 + 1/4 + 1/6 + 1/7 + 1/12 + 1/42
  418. No.418        1 = 1/3 + 1/4 + 1/6 + 1/7 + 1/14 + 1/28
  419. No.419        1 = 1/3 + 1/4 + 1/6 + 1/8 + 1/9 + 1/72
  420. No.420        1 = 1/3 + 1/4 + 1/6 + 1/8 + 1/10 + 1/40
  421. No.421        1 = 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24
  422. No.422        1 = 1/3 + 1/4 + 1/6 + 1/9 + 1/12 + 1/18
  423. No.423        1 = 1/3 + 1/4 + 1/6 + 1/10 + 1/12 + 1/15
复制代码
这是按字典排序输出的结果。
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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gxqcn
发表于 2011-9-12 21:39:48 | 显示全部楼层
数字最大（或字典序最小）的解：

$1/2+1/3+1/7+1/43+1/1807+1/3263442=1$

不知道数字最小的解是多少。
KeyTo9_Fans 发表于 2011-9-11 19:28


运行我的程序，结果确实如此。
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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geslon
发表于 2011-9-14 23:55:13 | 显示全部楼层
1分钟之内可以迅速找到一组解：

由于有 1=1/2+1/3+1/6    ------------------------------------(1)
的特性，又由于：
1=1/2+1/4+1/8+1/8      --------------------------------------(2)
将(1)两端乘以1/8,代入(2)式，就有：

1=1/2+1/4+1/8+1/16+1/24+1/48
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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wayne
发表于 2011-9-15 08:30:18 | 显示全部楼层
http://mathworld.wolfram.com/ZnamsProblem.html
毋因群疑而阻独见　　毋任己意而废人言
毋私小惠而伤大体　　毋借公论以快私情
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