AMC8 1996

AMC8 1996 · Q3

AMC8 1996 · Q3. It mainly tests Arithmetic sequences basics, Coordinate geometry.

The 64 whole numbers from 1 through 64 are written, one per square, on a checkerboard (an 8 by 8 array of 64 squares). The first 8 numbers are written in order across the first row, the next 8 across the second row, and so on. After all 64 numbers are written, the sum of the numbers in the four corners will be

从 1 到 64 的 64 个整数，每个方格一个，写在一个棋盘上（8×8 的 64 个方格）。前 8 个数字按顺序写在第一行，接下来的 8 个写在第二行，依此类推。写完所有 64 个数字后，四角数字的和是

(A) 130 130

(B) 131 131

(D) 133 133

(E) 134 134

Answer

Correct choice: (A)

正确答案：（A）

Solution

The first row is 1, 2, 3, …, 7, 8 and the last row is 57, 58, 59, …, 63, 64. Thus the four corner numbers are 1, 8, 57, and 64, and their sum is 130.

第一行是 1、2、3、…、7、8，最后一行是 57、58、59、…、63、64。因此四个角上的数字是 1、8、57 和 64，它们的和是 130。

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