Problem #35: Chinese Numbers

Think of a number between 1 and 26. Look at the following table of six squares, one square at a time.

+----------+----------+----------+
|  1  4  7 |  2  5  8 |  3  4  5 |
| 10 13 16 | 11 14 17 | 12 13 14 |
| 19 22 25 | 20 23 26 | 21 22 23 |
+----------+----------+----------+
|  6  7  8 |  9 10 11 | 18 19 20 |
| 15 16 17 | 12 13 14 | 21 22 23 |
| 24 25 26 | 15 16 17 | 24 25 26 |
+----------+----------+----------+

Each time the number you have picked belongs to one of the squares, write down the number in the top left-hand corner. Add together all these numbers.

For example, 16 is in the first, fourth, and fifth squares. If the first numbers of each of these squares are added together, we get 1 + 6 + 9 = 16, which is the original number we picked. Can you explain this?

[Top | Solution]