應該點計 THE PIGEONHOLE PRINCIPLE, E題諗唔掂......PLZ HELP!!!
2006-10-23 9:06 am
Twelve basketball players, whose uniforms are numbered 1 through 12, stand around the center ring on the court in an arbitrary arrangement. Show that some three consecutive players have the sum of their numbers at least 20.
回答 (2)
2006-10-23 9:32 am
✔ 最佳答案
設12個球員順時針的次序為A,B,C,D,E,F,G,H,I,J,K,L又設
A+B+C=a
B+C+D=b
C+D+E=c
...
L+A+B=l
每個球員的球衣號碼都出現3次
因此a+b+c+...+l=(1+2+3+...+12)x3=234
234 > 19 x 12 = 228
因此，即使a,b,c,...l 全部都是19，都不能湊夠234，亦即12個數的總和
因此起碼有一個a,b,c,...或l 大過或等於20
參考: ofcoz myself
2007-03-11 8:00 pm
點解o既???
而家係問sum of their numbers at least 20, 唔係問其中一個大過20 bor???!!!
而家係問sum of their numbers at least 20, 唔係問其中一個大過20 bor???!!!
收錄日期: 2021-04-12 17:23:56
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061023000051KK00261