標題:
發問:
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.
最佳解答:
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
其他解答:
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???!!!1C924F1C0172E337
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應該點計 THE PIGEONHOLE PRINCIPLE, E題諗唔掂......PLZ HELP!!!發問:
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.
最佳解答:
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
其他解答:
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???!!!1C924F1C0172E337
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