Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you find the chosen number from the grid using the clues?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
Follow the clues to find the mystery number.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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?
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?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you replace the letters with numbers? Is there only one solution in each case?
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 many trains can you make which are the same length as Matt's, using rods that are identical?
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?
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....?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
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?
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?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
In this matching game, you have to decide how long different events take.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
How many different triangles can you make on a circular pegboard that has nine pegs?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?