AMC10每日一题（2001年真题#10）

2001 AMC 10 竞赛试题/第10题

Problem

Consider the dark square in an array of unit squares, part of which is shown. The first ring of squares around this center square contains  unit squares. The second ring contains  unit squares. If we continue this process, the number of unit squares in the  ring is

Solutions

Solution 1

We can partition the  ring into  rectangles: two containing  unit squares and two containing  unit squares.

There are  unit squares in the  ring.

Thus, the  ring has  unit squares.

Solution 2 (Alternate Solution)

We can make the  ring by removing a square of side length  from a square of side length .

This ring contains  unit squares.

Thus, the  ring has  unit squares.