Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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.
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?
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?
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
What happens when you try and fit the triomino pieces into these
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.
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Can you cover the camel with these pieces?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Ben has five coins in his pocket. How much money might he have?
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.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
This dice train has been made using specific rules. How many different trains can you make?
Can you substitute numbers for the letters in these sums?
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
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?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Try this matching game which will help you recognise different ways of saying the same time interval.
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?
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?
Find all the numbers that can be made by adding the dots on two dice.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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.
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?