Divisibility

problem
Adding all nine

Age

11 to 14

Challenge level

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!
problem
American billions

Age

11 to 14

Challenge level

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
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
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
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
What numbers can we make?

Age

11 to 14

Challenge level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
problem
Counting factors

Age

11 to 14

Challenge level

Is there an efficient way to work out how many factors a large number has?
problem
Legs eleven

Age

11 to 14

Challenge level

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
problem
AB search

Age

11 to 14

Challenge level

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
problem
Peaches today, peaches tomorrow...

Age

11 to 14

Challenge level

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?