HMMT 二月 2002 · GEN2 赛 · 第 1 题

英文解析

1. The squares of a chessboard are numbered from left to right and top to bottom (sothat the first row reads 1 , 2 , . . . , 8, the second reads 9 , 10 , . . . , 16, and so forth). The number
   1 is on a black square. How many black squares contain odd numbers?
   Solution: 16 . The black squares in the n th row contain odd numbers when n is oddand even numbers when n is even; thus there are four rows where the black squares containodd numbers, and each such row contributes four black squares.