A man had to pack a sack of apples into packets but as each packet had to have exactly the same number of apples he was having difficulty.

If he packed 10 apples per packet, one packet only had 9.

If he packed 9 apples per packet, one packet only had 8.

If he packed 8 apples per packet, one packet only had 7.

If he packed 7 apples per packet, one packet only had 6.

And so on down to 2 apples.

How many apples did he start with?

Puzzle answer: Answer: 2519 apples.

The amount of apples divided by 10 leaves a remainder of 9, the amount of apples divided by 9 leaves a remainder of 8, etc. So we’re after a number of apples that divided by 10, 9, etc leaves a remainder of one less. This can be found by using the lowest/least common multiple of 10, 9, 8, 7, 6, 5, 4, 3 and 2, and then subtracting 1.