1992 APMO 第 5 题

Find a sequence of maximal length consisting of non-zero integers in which the sum of any seven consecutive terms is positive and that of any eleven consecutive terms is negative.

Answer: The maximum length is 16 . There are several possible sequences with this length; one such sequence is $(-7,-7,18,-7,-7,-7,18,-7,-7,18,-7,-7,-7,18,-7,-7)$.

找到一个由非零整数组成的最大长度序列，其中任意七个连续项的和为正，任意十一个连续项的和为负。

答：最大长度为 16 。这个长度有几种可能的序列；一个这样的序列是 $(-7,-7,18,-7,-7,-7,18,-7,-7,18,-7,-7,-7,18,-7,-7)$。