请教一题《数学难题精解》34

liul781

34. Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?

answer: 7

???please help and explain, thanks a lot!!

blackhorse

请搜索，已经很多讨论了，也有很不错的解释。

神经兮兮

把这10个数字中相加能得到10的每两个分成一组,其他的单列一组，可以分成6组 (1,9)(2,8)(3,7)(4,6)(5)(0)

最坏的情况 从中抽取的前6个数字来自不同的组 则这6个数字中没有两个相加和为10 而从剩下的4个数字中任意抽一个 必定能和前6个数字中的一个凑成10

所以答案是7个