This challenge encourages you to explore dividing a three-digit number by a single-digit number.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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.
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 activity involves rounding four-digit numbers to the nearest thousand.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
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?
Can you explain how this card trick works?
Delight your friends with this cunning trick! Can you explain how
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
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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?
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.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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 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?
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.
Pick a square within a multiplication square and add the numbers on
each diagonal. What do you notice?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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.
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?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
How many centimetres of rope will I need to make another mat just
like the one I have here?
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?
Find out what a "fault-free" rectangle is and try to make some of
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?
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Jo has three numbers which she adds together in pairs. When she
does this she has three different totals: 11, 17 and 22 What are
the three numbers Jo had to start with?”
A collection of games on the NIM theme
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.