Divisibility

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

Add powers of 3 and powers of 7 and get multiples of 11.

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.

When coins are put into piles of six 3 remain and in piles of eight 7 remain. How many remain when they are put into piles of 24?

What digit must replace the star to make the number a multiple of 11?