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

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The clues for this Sudoku are the product of the numbers in adjacent squares.

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Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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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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How many solutions can you find to this sum? Each of the different letters stands for a different number.

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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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Can you find a way to identify times tables after they have been shifted up or down?

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

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How many different symmetrical shapes can you make by shading triangles or squares?

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Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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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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What is the smallest number of answers you need to reveal in order to work out the missing headers?

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Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

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A game for 2 or more people, based on the traditional card game Rummy.

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A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

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If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

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Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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How many winning lines can you make in a three-dimensional version of noughts and crosses?

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Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

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A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

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Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

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

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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.

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There are nasty versions of this dice game but we'll start with the nice ones...

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My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

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What happens when you add a three digit number to its reverse?

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A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

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Find the frequency distribution for ordinary English, and use it to help you crack the code.

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Who said that adding, subtracting, multiplying and dividing couldn't be fun?

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Why not challenge a friend to play this transformation game?

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If you move the tiles around, can you make squares with different coloured edges?

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Where should you start, if you want to finish back where you started?

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Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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Engage in a little mathematical detective work to see if you can spot the fakes.

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Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

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Imagine you were given the chance to win some money... and imagine you had nothing to lose...

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Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

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Play around with sets of five numbers and see what you can discover about different types of average...

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Can you do a little mathematical detective work to figure out which number has been wiped out?