AMC 8 2000 Problem 12
AMC8 2000 年第 12 题
奇偶性★★★☆☆
A block wall 100 feet long and 7 feet high will be constructed using blocks that are 1 foot high and either 2 feet long or 1 foot long (no blocks may be cut). The vertical joins in the blocks must be staggered as shown, and the wall must be even on the ends. What is the smallest number of blocks needed to build this wall?
一堵墙 100 英尺长，7 英尺高，是由若干高度均为 1 英尺，长度为 2 英尺或者 1 英尺的砖块组成（不允许切割砖块）。砖块之间竖直的连接线必须如图所示交错开来，并且墙的两端要对齐。
则要建造这堵墙，需要的最少砖块数是多少？
- A.344
- B.347
- C.350
- D.353
- E.356
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
Since the bricks are 1 foot high, there will be 7 rows. To minimize the number of blocks used, rows 1, 3, 5, and 7 will look like the bottom row of the picture, which takes bricks to construct. Rows 2, 4, and 6 will look like the upper row pictured, which has 49 2-foot bricks in the middle, and 2 1-foot bricks on each end for a total of 51 bricks. Four rows of 50 bricks and three rows of 51 bricks totals bricks, giving the answer $D.$ If you wanted to be extra sure, you can realize that 700 / 2 = 350 blocks. However, this is impossible, as you need them to be staggered.
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