Edmund's Brainteasers
Problem 7
Solution
Problem 7: Andrew's bumper crop of apples. Solution
If Andrew had one more apple then he could have filled bags exactly with 2 apples, 3 apples, 4 apples, 5 apples, 6 apples, 7 apples and 8 apples. What is the smallest number with this property?
2 is the smallest number exactly divisible by 2
2 x 3 is the smallest number exactly divisible by 2 and 3
2 x 3 x 2 is the smallest number exactly divisible by 2, 3, 4
So, proceeding in this way, 2 x 3 x 2 x 5 x 7 x 2 = 840 is the smallest number exactly divisible by 2, 3, 4, 5, 6, 7, 8.
Andrew has 1 less than 840 apples, so he has 839 apples.