標題:
pigeonhole principle
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:
if no three consecutive players have the sum of their numbers at least 20, then the maximum value is 19 Generally speaking, for a circular arrangement, the total no of count of three consecutive players is 12 the maximum total values is 12*19= 228 however, from the other point of view, in the total combination of three consecutive players, each no [1,2...12] is counted three times total values =78*3=234 since 228 < 234 it is a contradiction
其他解答:63D0B758E2D502CC
pigeonhole principle
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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:
if no three consecutive players have the sum of their numbers at least 20, then the maximum value is 19 Generally speaking, for a circular arrangement, the total no of count of three consecutive players is 12 the maximum total values is 12*19= 228 however, from the other point of view, in the total combination of three consecutive players, each no [1,2...12] is counted three times total values =78*3=234 since 228 < 234 it is a contradiction
其他解答:63D0B758E2D502CC
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