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Can you find a way to identify times tables after they have been shifted up or down?
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
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?
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
There are nasty versions of this dice game but we'll start with the nice ones...
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
What can you see? What do you notice? What questions can you ask?
Play this game and see if you can figure out the computer's chosen number.
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
Why not challenge a friend to play this transformation game?
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
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?
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...
A game for 2 or more people, based on the traditional card game Rummy.
Can you find the values at the vertices when you know the values on the edges?
Can you work out what step size to take to ensure you visit all the dots on the circle?
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?
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.
If you move the tiles around, can you make squares with different coloured edges?
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?
Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
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?
How many different symmetrical shapes can you make by shading triangles or squares?
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Use these four dominoes to make a square that has the same number of dots on each side.