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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
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
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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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.
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
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.
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
Can you use the information to find out which cards I have used?
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 make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
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.
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
Can you coach your rowing eight to win?
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?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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.
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?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
A 3 digit number is multiplied by a 2 digit number and the
calculation is written out as shown with a digit in place of each
of the *'s. Complete the whole multiplication sum.
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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).
56 406 is the product of two consecutive numbers. What are these
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
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