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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Find out what a "fault-free" rectangle is and try to make some of
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
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.
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Delight your friends with this cunning trick! Can you explain how
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
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.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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?
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.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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
This challenge asks you to imagine a snake coiling on itself.
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?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This task follows on from Build it Up and takes the ideas into three dimensions!
Got It game for an adult and child. How can you play so that you know you will always win?
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?
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
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.
How many moves does it take to swap over some red and blue frogs? Do you have a method?
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?
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.
A collection of games on the NIM theme