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Problem 28


Problem 28


Number spiral diagonals

Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:s

**21** 22 23 24 **25** 20  **7**  8  **9** 10 19  6  **1**  2 11 18  **5**  4  **3** 12 **17** 16 15 14 **13**

It can be verified that the sum of the numbers on the diagonals is 101.

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?


螺旋数阵对角线

从1开始,按顺时针顺序向右铺开的5 × 5螺旋数阵如下所示:

**21** 22 23 24 **25** 20  **7**  8  **9** 10 19  6  **1**  2 11 18  **5**  4  **3** 12 **17** 16 15 14 **13**

可以验证,该数阵对角线上的数之和是101。

以同样方式构成的1001 × 1001螺旋数阵对角线上的数之和是多少?