Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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.
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.
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?
Can you make a 3x3 cube with these shapes made from small cubes?
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.
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
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 beat the computer in the challenging strategy game?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence 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?
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.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
Can you use the information to find out which cards I have used?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
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).
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?
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?
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?
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?
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.
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?
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?
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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.
Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?