# Divisibility Puzzle

Yesterday a friend of mine gave me this puzzle to solve :

Find a number consisting of 9 digits in which each of the digits from 1 to 9 appears only once. This number should satisfy the following requirements:

• The number should be divisible by 9.
• If the right-most digit is removed, the remaining number should be divisible by 8.
• If the two right-most digits are removed, the remaining number should be divisible by 7.
• If the three right-most digits are removed, the remaining number should be divisible by 6.
• If the eight right-most digits are removed, the remaining number should be divisible by 1.

We sure can solve this using crazy mathematics, but I have a clever idea, let the computer solve it for us.

How about writing code to solve this .. FUN \m/

When you break down this problem , its basically which permutation of 123456789 Â satisfy the above conditions.

So All we have to do is loop through all the permutations and for every permutation check if it satisfies the above conditions.

I know its not ideal to go through all the n! permutations and find the number. But it WORKS and it gave me solution in seconds.