Combinations

problem
Magic triangle

Age

7 to 11

Challenge level

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
problem
Even up

Age

11 to 14

Challenge level

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?
problem
Take three from five

Age

11 to 16

Challenge level

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
problem
Six times five

Age

11 to 14

Challenge level

How many six digit numbers are there which DO NOT contain a 5?
problem
Ladybirds in the garden

Age

5 to 7

Challenge level

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
problem
Sealed solution

Age

7 to 11

Challenge level

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
problem
Penta primes

Age

7 to 11

Challenge level

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?
problem
Penta post

Age

7 to 11

Challenge level

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
problem
Throw a 100

Age

7 to 11

Challenge level

Can you score 100 by throwing rings on this board? Is there more than way to do it?
problem
Plates of biscuits

Age

7 to 11

Challenge level

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?