HMMT 二月 2004 · 团队赛 · 第 6 题

英文解析

6. Prove that the number of odd numbers in row n is at most twice the number of switchpairs in row n − 1.
   Solution: Each odd number in row n is the sum of two of the three numbers above itin row n − 1; these three numbers cannot all have the same parity (or else any sum oftwo of them would be even), so somewhere among them is a switch pair. Since eachswitch pair in row n − 1 can contribute to at most two odd numbers in row n in thismanner (namely, the two numbers immediately below the members of the pair), the result follows.