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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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Is there an efficient way to work out how many factors a large number has?

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

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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 three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

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

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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?

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

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

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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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The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

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

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Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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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?

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Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.

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

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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?

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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 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.

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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?

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.

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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.

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

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Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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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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Surprise your friends with this magic square trick.

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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.

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

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

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This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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

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

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Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

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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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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?