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?

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 find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

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?

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?

Can you make a 3x3 cube with these shapes made from small cubes?

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?”

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?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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.

A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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).

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?

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?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

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?

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 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.

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. Is it possible to fill every seat and take exactly £100?

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 use the information to find out which cards I have used?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

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?

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?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

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?

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 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?

56 406 is the product of two consecutive numbers. What are these two numbers?

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?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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?

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.

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?