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.
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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.
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. Use the information to find out how many discs of each colour there are in the box.
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?
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?
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.
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.
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 use the information to find out which cards I have used?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
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?
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?
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
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?
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?
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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.
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
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 your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
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?
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Use the information to work out how many gifts there are in each pile.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
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?
Can you number the vertices, edges and faces of a tetrahedron so that the number on each edge is the mean of the numbers on the adjacent vertices and the mean of the numbers on the adjacent faces?
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.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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.
56 406 is the product of two consecutive numbers. What are these two numbers?
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).
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?
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.