Divisibility

problem
Going round in circles

Age

11 to 14

Challenge level

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
problem
Power mad!

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

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

Age

11 to 14

Challenge level

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

Age

16 to 18

Challenge level

Add powers of 3 and powers of 7 and get multiples of 11.
problem
There's always one isn't there

Age

14 to 16

Challenge level

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.
problem
Odd stones

Age

14 to 16

Challenge level

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.
problem
Coin collection

Age

14 to 16

Challenge level

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?
problem
Missing digit

Age

11 to 14

Challenge level

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