Challenge Level

9 5 ___ ___

9 5 ___ (0 or 5) (since divisible by 5)

9 5 ___ 0 (divisible by 6, so even)

Divisible by 3 $\Rightarrow$ sum of digits a multiple of 3

9 + 5 = 14, so this digit can be 1, 4 or 7

9510, 9540 or 9570

Divisible by 4 $\Rightarrow$ last 2 digits divisible by 4

9540

The number is divisible by 3, 4, 5 and 6, so it is divisible by 60 (lowest common multiple).

The number is less than 9600. 96 = 60 + 36, so 96 is a multiple of 6, so 960 is a multiple of 60 and therefore 9600 is a multiple of 60.

Multiples of 60: 9600, 9540, 9480

Only 9540 begins 95.

You can find more short problems, arranged by curriculum topic, in our short problems collection.