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.
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
Can you find a path from a number at the top of this network to the
bottom which goes through each number from 1 to 9 once and once
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?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
56 406 is the product of two consecutive numbers. What are these
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?
There are a number of coins on a table.
One quarter of the coins show heads.
If I turn over 2 coins, then one third show heads. How many coins are there altogether?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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.
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
In 1871 a mathematician called Augustus De Morgan died. De Morgan
made a puzzling statement about his age. Can you discover which
year De Morgan was born in?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
There were 22 legs creeping across the web. How many flies? How many spiders?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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?
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).
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
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?
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
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
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.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
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
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?
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?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
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.
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
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 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?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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 numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you go from A to Z right through the alphabet in the hexagonal