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?
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?
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.
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.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
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?
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?
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?
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
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?
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
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.
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?
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.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
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?
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).
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?
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.
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.
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Can you make a 3x3 cube with these shapes made from small cubes?
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?
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?
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?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
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?
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.