送交者: 草绿 于 July 29, 2009 13:03:51:
回答: 对，应该是一致的。 由 老椰子 于 July 28, 2009 18:39:00:
这个题的结果其实就是generalized pigeonhole principle:
if n discrete objects are to be allocated to m containers, then at least one container must hold no fewer than [n/m] objects, where [x] is the ceiling function, denoting the smallest integer larger than or equal to x. (BTW, 这个叙述 "at least one container must hold" 好像比你上面那个简单易懂:))
For the present problem, we can consider each color in one room as a hole, then the total number of holes m=# of colors X # of rooms, thus the answer is total # of people/total # of holes.
There are some cases where this principle can be applied. One example I saw online is: if there are 6 people at a party, then either 3 of them knew each other before the party or 3 of them were complete strangers before the party.
As to the proof of this principle, 我想反证很容易, 既如果所有的holes都hold fewer than [n/m] objects, then the total sum, that is, the total number of objects will be less than n.