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

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I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

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Play this game and see if you can figure out the computer's chosen number.

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Join pentagons together edge to edge. Will they form a ring?

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In this game you are challenged to gain more columns of lily pads than your opponent.

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L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

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Collect as many diamonds as you can by drawing three straight lines.

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Can you work out what step size to take to ensure you visit all the dots on the circle?

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Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

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Have a go at this version of John Conway's game. Do you have any good strategies for winning?

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Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

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It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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Here is a chance to play a version of the classic Countdown Game.

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Here are two games you can play. Which offers the better chance of winning?

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Can you find a strategy that ensures you get to take the last biscuit in this game?

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A game in which players take it in turns to choose a number. Can you block your opponent?

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This interactivity is designed to help you gain a better understanding of how your lifestyle choices can affect your carbon footprint.

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Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

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Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

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Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

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Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

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A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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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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Can you find the hidden factors which multiply together to produce each quadratic expression?

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In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

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In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

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How many moves does it take to swap over some red and blue frogs? Do you have a method?

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The Number Jumbler can always work out your chosen symbol. Can you work out how?

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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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Four friends must cross a bridge. How can they all cross it in just 17 minutes?