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?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
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?
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
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.
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Ben has five coins in his pocket. How much money might he have?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
This challenge is about finding the difference between numbers which have the same tens digit.
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
How many trapeziums, of various sizes, are hidden in this picture?
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.
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?
Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
What could the half time scores have been in these Olympic hockey matches?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.
Find all the numbers that can be made by adding the dots on two dice.
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
My coat has three buttons. How many ways can you find to do up all the buttons?
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Can you find the chosen number from the grid using the clues?
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?