Question

Zhou 先生把从 $1$ 到 $225$ 的所有整数放入一个 $15$ 行 $15$ 列的方格中。他把 $1$ 放在正中间的方格（第八行第八列），然后如图所示按顺时针方向逐个放入其他数。在从上往下数第二行中出现的最大数与最小数之和是多少？

Mr. Zhou places all the integers from $1$ to $225$ into a $15$ by $15$ grid. He places $1$ in the middle square (eighth row and eighth column) and places other numbers one by one clockwise, as shown in part in the diagram below. What is the sum of the greatest number and the least number that appear in the second row from the top?

$367$

$368$

$369$

$379$

$380$

答案：A

知识点：找规律完全平方数

难度评级：1420

视频讲解：

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文字解答：

在外层 $15\times15$ 的一圈中，最上面一行包含 $211,212,\ldots,225$ ，因此第二行中正好在 $211$ 下方的数是 $210$ 。

这是第二行的最大数。内层 $13\times13$ 螺旋的右上角是 $13^2=169$ 。在整个方格第二行中，内层这一行的数从 $157$ 到 $169$ ，因此最小数是 $157$ 。

所求和为 $210+157=367$ 。

所以答案是 A。

In the outer $15\times15$ ring, the top row contains $211,212,\ldots,225,$ so the number just below $211$ in the second row is $210.$ This is the greatest number in the second row.

The inner $13\times13$ spiral has $13^2=169$ in its upper-right corner. In the second row of the full grid, the inner-ring entries run from $157$ to $169.$ Thus the least entry in that row is $157.$

The required sum is $210+157=367.$

Thus, the answer is A .

2021 AMC 10B Spring 第 8 题

答案：A

难度评级：1420

视频讲解：

文字解答：

其他年份的第 8 题