This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
This challenge asks you to imagine a snake coiling on itself.
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.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative 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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Can you explain how this card trick works?
Delight your friends with this cunning trick! Can you explain how
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.
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.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
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.
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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.
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Can you tangle yourself up and reach any fraction?
Can you find the values at the vertices when you know the values on
It would be nice to have a strategy for disentangling any tangled
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
A collection of games on the NIM theme
What would be the smallest number of moves needed to move a Knight
from a chess set from one corner to the opposite corner of a 99 by
99 square board?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable.
Decide which of these diagrams are traversable.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?