![](https://cdn.mathpix.com/cropped/2024_05_06_e0ce4a33d8b15522751eg-08.jpg?height=133&width=2056&top_left_y=1777&top_left_x=-2)

If 6 is subtracted from a certain three-digit number, it will be divisible by 7; if 7 is subtracted, it will be divisible by 8; and if 8 is subtracted, it will be divisible by 9.

Determine this number.
What will happen if you add one to the desired number?

## Solution

If you add 1 to the desired number, it will be divisible by $7 \cdot 8 \cdot 9=504$. Since the number is a three-digit number, there is only one possibility - it is equal to

$503=7 \cdot 8 \cdot 9-1$.

## Answer

503.