This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
This challenge is about finding the difference between numbers which have the same tens digit.
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
A game for 2 people. Take turns placing a counter on the star. You
win when you have completed a line of 3 in your colour.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Find all the numbers that can be made by adding the dots on two dice.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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.
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
Ben has five coins in his pocket. How much money might he have?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Can you find all the different ways of lining up these Cuisenaire
Find out what a "fault-free" rectangle is and try to make some of
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
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?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
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?