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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
This challenge is about finding the difference between numbers which have the same tens digit.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Find out what a "fault-free" rectangle is and try to make some of
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Got It game for an adult and child. How can you play so that you know you will always win?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
This task follows on from Build it Up and takes the ideas into three dimensions!
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
Can you find all the ways to get 15 at the top of this triangle of numbers?
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.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
What happens when you round these three-digit numbers to the nearest 100?
This activity focuses on rounding to the nearest 10.
This activity involves rounding four-digit numbers to the nearest thousand.
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
An investigation that gives you the opportunity to make and justify
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Find the sum of all three-digit numbers each of whose digits is
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind