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.
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
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?
It would be nice to have a strategy for disentangling any tangled ropes...
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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.
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 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.
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.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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.
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 ï¿½ 1 [1/3]. What other numbers have the sum equal to the product and can this be. . . .
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
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.
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.
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
A collection of games on the NIM theme
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Got It game for an adult and child. How can you play so that you know you will always win?
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.
Can you find the values at the vertices when you know the values on the edges?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
This challenge asks you to imagine a snake coiling on itself.
Try out this number trick. What happens with different starting numbers? What do you notice?
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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.
Can you explain the strategy for winning this game with any target?
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
This task follows on from Build it Up and takes the ideas into three dimensions!
Find the sum of all three-digit numbers each of whose digits is odd.
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
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?
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?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
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?