Earlier today I set you the following problem from the international maths Kangaroo, a multiple choice challenge taken by more than seven million children every year. (For more details about this extraordinary event see the original story .)

Here is is again with the solution.

The four powers

A four digit number abcd satisfies the equation abcd = a a + b b + c c + d d .

What is a ?

2

3

4

5

6

[Note: abcd means that the first digit is a , the second is b , the third is c and the fourth is d . It does not mean a x b x c x d . The numbers a, b, c and d do not have to be different.]

As an extra, what are b , c and d ?

Solution abcd = 3435

Workings

Let’s first list the values of x x for x = 1 to 6.

1 1 = 1, 2 2 = 4, 3 3 = 27, 4 4 = 256, 5 5 = 3125, 6 6 > 9999.

I didn’t calculate the exact value of 6 6 , because as soon as I realised it was greater than a four digit number I knew I had an upper bound for the values of a, b, c and d.…