This challenge is about finding the difference between numbers which have the same tens digit.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this 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?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Ben’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?
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?
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.
Got It game for an adult and child. How can you play so that you know you will always win?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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.
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
This challenge asks you to imagine a snake coiling on itself.
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
It starts quite simple but great opportunities for number discoveries and patterns!
Can you dissect an equilateral triangle into 6 smaller ones? What
number of smaller equilateral triangles is it NOT possible to
dissect a larger equilateral triangle into?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
This activity involves rounding four-digit numbers to the nearest thousand.
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
What happens when you round these three-digit numbers to the nearest 100?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
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.
This activity focuses on rounding to the nearest 10.
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?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
What happens when you round these numbers to the nearest whole number?
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.