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.
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?
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?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Can you make a 3x3 cube with these shapes made from small cubes?
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
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?
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?
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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.
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you guess the colours of the 10 marbles in the bag? Can you
develop an effective strategy for reaching 1000 points in the least
number of rounds?
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.
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
Three teams have each played two matches. The table gives the total
number points and goals scored for and against each team. Fill in
the table and find the scores in the three matches.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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 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
Imagine picking up a bow and some arrows and attempting to hit the
target a few times. Can you work out the settings for the sight
that give you the best chance of gaining a high score?
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.
56 406 is the product of two consecutive numbers. What are these
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
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?
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).
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
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?