[其他] 鴿籠

[mqazz1 (無法顯示)]

1. Show that given any set of 5 integers, there are 3 integers in the set

whose sume is divisible by 3


2. A wheel of fortune has the integers from 1 to 25 placed on it in a random

manner. Show that regardless of how the numbers are positioned on the wheel,

there are three adjacent numbers whose sum is at least 39


請問這兩題有人會其中一題或兩題都會的嗎?

謝謝

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推 ss1132      :1.想成1,0,-1三類這三類每種都不能挑到三個
→ ss1132      :因此最多1,1,0,0,-1,-1但三類不能同時出現
→ ss1132      :因此要避開和為3倍數只能型如1,1,0,0
→ ss1132      :所以第五個加進來一定湊得到
推 yusd24      :2.假設不然, 則(1+2+..+25)<39*25/3 矛盾