Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
Can you make a 3x3 cube with these shapes made from small cubes?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you beat the computer in the challenging strategy game?
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?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
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.
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?
Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
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).
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Can you use the information to find out which cards I have used?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?
What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
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?
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.
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.
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
Use these four dominoes to make a square that has the same number of dots on each side.
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
In 1871 a mathematician called Augustus De Morgan died. De Morgan made a puzzling statement about his age. Can you discover which year De Morgan was born in?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
56 406 is the product of two consecutive numbers. What are these two numbers?
Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?