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?
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?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
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?
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?”
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
Can you beat the computer in the challenging strategy game?
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.
Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?
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?
Use the information to work out how many gifts there are in each pile.
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.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
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?
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.
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?
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?
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?
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?
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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.
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
Can you make a 3x3 cube with these shapes made from small cubes?
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?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Can you use the information to find out which cards I have used?
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).
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
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?
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
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.