Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
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?
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.
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?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
Use the clues to colour each square.
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?
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.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
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?
How many different rectangles can you make using this set of rods?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
How will you go about finding all the jigsaw pieces that have one peg and one hole?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Ben has five coins in his pocket. How much money might he have?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
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!
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
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.
Find all the numbers that can be made by adding the dots on two dice.
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?