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.
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.
This challenge asks you to imagine a snake coiling on itself.
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
A package contains a set of resources designed to develop
pupils’ mathematical thinking. This package places a
particular emphasis on “generalising” and is designed
to meet the. . . .
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?
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?
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
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Got It game for an adult and child. How can you play so that you know you will always win?
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.
It starts quite simple but great opportunities for number discoveries and patterns!
A collection of games on the NIM theme
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?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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?
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.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This challenge is about finding the difference between numbers which have the same tens digit.
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 encourages you to explore dividing a three-digit number by a single-digit number.
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?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
This activity involves rounding four-digit numbers to the nearest thousand.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
What happens when you round these numbers to the nearest whole number?
This activity focuses on rounding to the nearest 10.
What happens when you round these three-digit numbers to the nearest 100?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
How can you arrange these 10 matches in four piles so that when you
move one match from three of the piles into the fourth, you end up
with the same arrangement?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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
Find the sum of all three-digit numbers each of whose digits is
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?