Number Detective

Follow the clues to find the mystery number.

Six Is the Sum

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

(w)holy Numbers

A church hymn book contains 700 hymns. The numbers of the hymns are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?

Diagonal Sums

Stage: 2 Challenge Level:

Here is a $100$ square with some of the numbers shaded:

Look at the green square which contains the numbers $2, 3, 12$ and $13$.
What is the sum of the numbers that are diagonally opposite each other?
Do you notice anything?
Look at the pink square.
Does the same thing happen?
Look at the squares shaded red. They form the corners of a large $3$ by $3$ square.