You have 5 darts and your target score is 44. How many different ways could you score 44?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
Investigate the different distances of these car journeys and find out how long they take.
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
How would you count the number of fingers in these pictures?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
Here is a chance to play a version of the classic Countdown Game.
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
This is an adding game for two players.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Find a great variety of ways of asking questions which make 8.
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
This task follows on from Build it Up and takes the ideas into three dimensions!
What is the sum of all the three digit whole numbers?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
What is happening at each box in these machines?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.