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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Here is a chance to play a fractions version of the classic Countdown Game.
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 article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
This is an adding game for two players.
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
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?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?
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?
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.
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?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
This task follows on from Build it Up and takes the ideas into three dimensions!
How many different differences can you make?
Here is a chance to play a version of the classic Countdown Game.
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?
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.
Surprise your friends with this magic square trick.
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
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?
This Sudoku requires you to do some working backwards before working forwards.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Number problems at primary level that may require resilience.
What is happening at each box in these machines?
This Sudoku, based on differences. Using the one clue number can you find the solution?
How would you count the number of fingers in these pictures?