A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Try this matching game which will help you recognise different ways of saying the same time interval.
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
Lorenzie was packing his bag for a school trip. He packed four
shirts and three pairs of pants. "I will be able to have a
different outfit each day", he said. How many days will Lorenzie be
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
Find out what a "fault-free" rectangle is and try to make some of
In this matching game, you have to decide how long different events take.
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
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 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
My coat has three buttons. How many ways can you find to do up all
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you fill in the empty boxes in the grid with the right shape
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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 is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Can you find all the different triangles on these peg boards, and
find their angles?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Find all the numbers that can be made by adding the dots on two dice.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Find out about Magic Squares in this article written for students. Why are they magic?!