## 163. The Cat and the Mouse.

- One of these barrels has a mouse in it,- said the dog.
- Which one? - asked the cat.
- Well, the five hundredth.
- What do you mean by that? There are only five barrels here.
- The barrel I mean will be the five hundredth if you start counting forward and backward like this.

And the dog explained how exactly one should count:

| 1 | 2 | 3 | 4 | 5 |
| ---: | ---: | ---: | ---: | ---: |
| 9 | 8 | 7 | 6 |  |
|  | 10 | 11 | 12 | 13 |

For example, the seventh barrel will coincide with the one that has the number 3, and the twelfth barrel with the one that has the number 4.

- This will take a lot of time,- said the cat and began to count patiently. Several times she got confused and started all over again.
- Damn it!-exclaimed the dog.-Hurry up, or it will be too late!
- Be damned yourself! You made me lose my count again, now I have to start all over.

Meanwhile, the mouse, having heard the entire conversation, gnawed a hole and slipped away just as the cat jumped into the right barrel.

- I knew it would happen, - said the dog. - Your education I would not dare to call too brilliant. A little familiarity with arithmetic would not hurt any cat, just as it does not hurt any dog. What am I saying! Even some snakes are so diligent in this science that they have to wear glasses!

Which of the barrels was the five hundredth? Could you find the answer without counting to 500?

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-049.jpg?height=354&width=628&top_left_y=1228&top_left_x=720)
163. You just need to divide the given number by 8. If it divides evenly, with no remainder, the mouse is in the second barrel. If the remainder is 1, 2, 3, 4, or 5, the barrel number will match this remainder. If the remainder is greater than 5, subtract it from 10. The resulting difference is the barrel number. The number 500, when divided by 8, gives a remainder of 4, so the number on the sought-after barrel is 4.