Question

数字 $1,2,3,4,5,6,7,8,9$ 被写入一个 $3\times3$ 方格阵列中，每格一个数，并且若两个数连续，则它们所在的方格共边。四个角上的数字和为 $18$ 。中心格中的数字是多少？

All the numbers $1,2,3,4,5,6,7,8,9$ are written in a $3\times3$ array of squares, one number in each square, in such a way that if two numbers are consecutive then they occupy squares that share an edge. The numbers in the four corners add up to $18.$ What number is in the center?

$5$

$6$

$7$

$8$

$9$

答案：C

知识点：奇偶性逻辑推理

难度评级：1590

解答：

像棋盘一样染色，使四个角和中心同色。由于连续数字位于相邻的异色格中，沿数字链颜色交替，所以这五个同色格中是五个奇数 $1,3,5,7,9$ 其和为 $25$ 四个角的和为 $18$ ，所以中心格中的数为 $25-18=7$ 。

所以正确答案是 C。

Color the grid like a checkerboard so the four corners and the center share one color. Since consecutive numbers occupy adjacent (opposite colored) squares, the numbers alternate parity along the chain, so the five same-colored cells contain the five odd numbers $1,3,5,7,9,$ which sum to $25.$ The four corners add to $18,$ so the center is $25-18=7.$

Thus, the correct answer is C.

2016 AMC 12B 第 12 题

答案：C

难度评级：1590

解答：

其他年份的第 12 题