[理工] [離散]-鴿籠原理

看板Grad-ProbAsk作者amidofun (amido)時間16年前 (2010/01/09 02:05)推噓2(2推 0噓 2→)

留言4則, 4人參與討論串1/4 (看更多)

There are 20 students in a class, all born on different days of January, 1980. Show that there are two students born on the ith day and the jth day of January with│i-j│= 8. 我的想法是把一月分堆,如下: {01,09},{02,10},{03,11},{04,12},{05,13},{06,14},{07,15},{08,16}:1號~16號 {17,25},{18,26},{19,27},{20,28},{21,29},{22,30},{23,31},{24}:17號~31號共16組根據鴿籠定理,20個學生必有4組絕對值的差等於8.... 但題目只要求2個學生，即一組,那我這樣的證法有誤嗎? 這算暴力分堆法嗎= =?因為題庫班上的方法我比較不懂還是我誤解題意了? -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 218.32.100.18

推

converse2006

01/09 02:13, , 1^F

01/09 02:13, 1^F

→

amidofun

01/09 02:19, , 2^F

01/09 02:19, 2^F

→

doom8199

01/09 02:23, , 3^F

01/09 02:23, 3^F