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?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
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!
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
Find the sum of all three-digit numbers each of whose digits is odd.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?
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?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
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!
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?
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
You have 5 darts and your target score is 44. How many different ways could you score 44?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
This challenge is about finding the difference between numbers which have the same tens digit.
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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
This task follows on from Build it Up and takes the ideas into three dimensions!
Investigate what happens when you add house numbers along a street in different ways.
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?
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
These two group activities use mathematical reasoning - one is numerical, one geometric.
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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 possible?
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?
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?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
This is an adding game for two players.
Can you substitute numbers for the letters in these sums?
Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?