Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
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?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
There were 22 legs creeping across the web. How many flies? How many spiders?
All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you go from A to Z right through the alphabet in the hexagonal maze?
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
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.
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you use the information to find out which cards I have used?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
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?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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.
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?
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.
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?
Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?
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?
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?
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 make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?
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?
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.
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.
You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?