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.
This challenge asks you to imagine a snake coiling on itself.
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
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.
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?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
An investigation that gives you the opportunity to make and justify
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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 the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Find out what a "fault-free" rectangle is and try to make some of
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?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
This challenge is about finding the difference between numbers which have the same tens digit.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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 activity focuses on rounding to the nearest 10.
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?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
A collection of games on the NIM theme
This activity involves rounding four-digit numbers to the nearest thousand.
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?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
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.
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?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Find the sum of all three-digit numbers each of whose digits is
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
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?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
What happens when you round these three-digit numbers to the nearest 100?
What happens when you round these numbers to the nearest whole number?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?