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.

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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?

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?

If you have only four weights, where could you place them in order to balance this equaliser?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Here is a chance to play a version of the classic Countdown Game.

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

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?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

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.

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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.

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?

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!

Using the statements, can you work out how many of each type of rabbit there are in these pens?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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?

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.

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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.

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

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?

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?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

You have 5 darts and your target score is 44. How many different ways could you score 44?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Got It game for an adult and child. How can you play so that you know you will always win?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?