Nim-7 game for an adult and child. Who will be the one to take the last counter?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
Got It game for an adult and child. How can you play so that you know you will always win?
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
This challenge asks you to imagine a snake coiling on itself.
This challenge is about finding the difference between numbers which have the same tens digit.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
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.
Here are two kinds of spirals for you to explore. What do you notice?
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 is a game for two players. Can you find out how to be the first to get to 12 o'clock?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
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
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?
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
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.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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 encourages you to explore dividing a three-digit number by a single-digit number.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
A game for 2 players with similaritlies to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.
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
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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 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.
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?
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?