Let's start by drawing lines from some of the utilities to some of the houses: gas -> house 1 -> electricity -> house 2 -> water -> house 3. | |
If we draw one more line, from house 3 to the gas company, then we have a loop. Notice that our loop has an inside and an outside. |
That means two lines will have to be either outside or inside the loop. These two lines will have to cross. |
That means the boundary of a face could either be house 1 - utility 1 - house 2 - utility 2 (four edges): | |
or house 1 - utility 1 - house 2 - utility 2 - house 3 - utility 3 (six edges): |
原帖由 pontifex 于 2007-9-7 12:32 发表
我给一个浅显一点的证明吧:拿出纸笔画一下.
把房子进行编号,叫做1,2,3;而水,电,气分别用A,B,C代替.
首先,只考虑1,2,A,B.可知这四个元素必然会连成一个封闭环.(1-A-2-B).这个环有四条边.
现在把C ...
Version I: Can three houses be connected to three utilities concurrently, without the pipes crossing on any dimensional plane? Version II: Draw this puzzle on a piece of paper, and without lifting the pen from the paper or crossing lines, connect the utilities to the three houses. |
Let's start by drawing lines from some of the utilities to some of the houses: gas -> house 1 -> electricity -> house 2 -> water -> house 3. | |
If we draw one more line, from house 3 to the gas company, then we have a loop. Notice that our loop has an inside and an outside. |
That means two lines will have to be either outside or inside the loop. These two lines will have to cross. |
That means the boundary of a face could either be house 1 - utility 1 - house 2 - utility 2 (four edges): | |
or house 1 - utility 1 - house 2 - utility 2 - house 3 - utility 3 (six edges): |
原帖由 caily 于 2007-9-9 08:25 发表
不是我这人直肠子,为得一个鼠标,出那么难的题,老吴你也太抠了。如果我这个答案有效的话,就把鼠标送我女朋友吧,我在剑桥先谢谢您了。嘎嘎嘎嘎
16904
这道题是英国最有名的谜题专家Henry Ernest Dud ...
原帖由 caily 于 2007-9-9 08:25 发表
不是我这人直肠子,为得一个鼠标,出那么难的题,老吴你也太抠了。如果我这个答案有效的话,就把鼠标送我女朋友吧,我在剑桥先谢谢您了。嘎嘎嘎嘎
16904
这道题是英国最有名的谜题专家Henry Ernest Dud ...
原帖由 pontifex 于 2007-9-7 13:15 发表
老吴还卖关子!我看不下去了!
1。http://www.supuzzle.com/supuzzle.html
这是题目的出处,是flash格式,可以在线玩。大家可以在线去玩玩!
2。http://mathforum.org/dr.math/faq/faq.3utilities.html
...
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