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?
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Can you coach your rowing eight to win?
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 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
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?
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.
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.
This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.
Use these four dominoes to make a square that has the same number of dots on each side.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?
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?
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.
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 make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?
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?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Can you use the information to find out which cards I have used?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
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?
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?
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?
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.
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
The discs for this game are kept in a flat square box with a square hole for each disc. 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.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.
56 406 is the product of two consecutive numbers. What are these two numbers?
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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?
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).