推 sansia :請問是哪本書? 08/16 12:09
→ weeeeeeeeell:交通大學應數系用的那本 08/16 12:42
推 sansia :那是哪一本? 08/16 14:21
※ 引述《sansia (sansia)》之銘言：
: 某象棋棋士一連比賽了11 個星期，他的戰績輝煌，這11 個星期的紀錄如下：
: 每日至少勝1 次；每星期最多勝12 次。由此紀錄可推得必存在一段連續的日子
: （連續k 天，1 k 77）裏，此棋士不多不少剛好勝了21 次。試證明之。
: 試利用上面例，推導出一個用途較廣的定理，而使得其中之部分數值改以
: 變數（參數）表示。
你的題目是出自離散數學課本鴿籠原理那一章
原文如下
A chess master who has 11 weeks to prepare for a tournament decides to
play at least one game every day but, to avoid tiring himself, he decides
no to play more than 12 games during any calendar week. Show that there
exists a succession of (consecutive) days during which the chess master
will have played exactly 21 games.
Let a_1 be the number of games played on the first day, a_2 the total
number of games played on the first and second days, a_3 .....
... Therefore, on days j+1, j+2,.. i the chess master played a total of
21 games.
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