Question

要建造一面长 $100$ 英尺、高 $7$ 英尺的砌块墙，使用的砌块高 $1$ 英尺，长度可以是 $2$ 英尺或 $1$ 英尺（不得切割砌块）。砌块的竖缝必须如图所示错开，且墙两端必须齐平。建造这面墙最少需要多少块砌块？

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?

$344$

$347$

$350$

$353$

$356$

答案：D

知识点：最优化

难度评级：1220

解答：

墙共有 $7$ 行，每行高 $1$ 英尺。

为了使用最少砌块，第 $1, 3, 5$ 和 $7$ 行可采用图中底行的模式，每行需要 $50$ 块砌块。

第 $2, 4$ 和 $6$ 行采用图中上行的模式，中间有 $49$ 块 $2$ 英尺砌块，两端各有一块 $1$ 英尺砌块，共 $51$ 块砌块。

将 $4$ 行 $50$ 块和 $3$ 行 $51$ 块相加，得到 $4 \cdot 50 + 3 \cdot 51 = 200 + 153 = 353$ 块砌块。

所以正确答案是 D。

The total number of rows in the wall is $7,$ with each row being $1$ foot high.

To use the minimum number of bricks, rows $1, 3, 5,$ and $7$ will have the same pattern as the bottom row in the picture, which requires $50$ bricks to construct.

Rows $2, 4,$ and $6$ will have the same pattern as the upper row in the picture, which has $49$ $2$ -foot bricks in the middle and one $1$ -foot brick on each end, for a total of $51$ bricks.

When you add up $4$ rows of $50$ bricks and $3$ rows of $51$ bricks, you get a total of $4 \cdot 50 + 3 \cdot 51 = 200 + 153 = 353$ bricks.

Thus, D is the correct answer.

2000 AMC 8 第 12 题

答案：D

难度评级：1220

解答：

其他年份的第 12 题