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.
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Can you explain how this card trick works?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.
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.
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.
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Can you find sets of sloping lines that enclose a square?
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.
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Got It game for an adult and child. How can you play so that you know you will always win?
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Delight your friends with this cunning trick! Can you explain how it works?
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.
A collection of games on the NIM theme
Can you find the values at the vertices when you know the values on the edges?
We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
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?
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.
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 moves.
Can all unit fractions be written as the sum of two unit fractions?
The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
A game for 2 players with similarities 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.
It starts quite simple but great opportunities for number discoveries and patterns!
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?
Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
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?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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 maths trails.
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
It would be nice to have a strategy for disentangling any tangled ropes...
Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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 little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .
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?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...