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Can you work out how to win this game of Nim? Does it matter if you go first or second?

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Nim-7 game for an adult and child. Who will be the one to take the last counter?

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Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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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.

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.

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Can you explain the strategy for winning this game with any target?

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Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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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.

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Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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Delight your friends with this cunning trick! Can you explain how it works?

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Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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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.

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Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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.

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

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Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

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Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I. . . .

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Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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Can you find the values at the vertices when you know the values on the edges?

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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.

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Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

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Can all unit fractions be written as the sum of two unit fractions?

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Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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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?

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In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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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.

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This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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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.

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This task follows on from Build it Up and takes the ideas into three dimensions!

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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?

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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?

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This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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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. . . .

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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?

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Got It game for an adult and child. How can you play so that you know you will always win?

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Are these statements always true, sometimes true or never true?

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An investigation that gives you the opportunity to make and justify predictions.

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Here are two kinds of spirals for you to explore. What do you notice?

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Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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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

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Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

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When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...