Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This task follows on from Build it Up and takes the ideas into three dimensions!
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
An investigation that gives you the opportunity to make and justify predictions.
While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Try out this number trick. What happens with different starting numbers? What do you notice?
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.
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.
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.
It starts quite simple but great opportunities for number discoveries and patterns!
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
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 happens?
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 explain the strategy for winning this game with any target?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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 make dice stairs using the rules stated? How do you know you have all the possible stairs?
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
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.
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?
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Surprise your friends with this magic square trick.
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Got It game for an adult and child. How can you play so that you know you will always win?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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. . . .
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
What happens when you round these three-digit numbers to the nearest 100?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
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.
Can you find the values at the vertices when you know the values on the edges?
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?