Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Here are some rods that are different colours. How could I make a yellow rod using white and red rods?
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
Use the clues to colour each square.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
What happens when you try and fit the triomino pieces into these two grids?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
How will you go about finding all the jigsaw pieces that have one peg and one hole?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Can you cover the camel with these pieces?
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
Can you find the chosen number from the grid using the clues?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
What is the best way to shunt these carriages so that each train can continue its journey?
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
How many different rectangles can you make using this set of rods?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?