Use these four dominoes to make a square that has the same number of dots on each side.
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
Make one big triangle so the numbers that touch on the small triangles add to 10.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Can you make a 3x3 cube with these shapes made from small cubes?
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
You have a set of the digits from 0 – 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?
Can you find a path from a number at the top of this network to the bottom which goes through each number from 1 to 9 once and once only?
What do you notice about these squares of numbers? What is the same? What is different?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
Using only six straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).
If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
Can you use the information to find out which cards I have used?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?
Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?