This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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 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!
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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 jugs.
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!
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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
This dice train has been made using specific rules. How many different trains can you make?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
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.
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
What could the half time scores have been in these Olympic hockey matches?
Can you make square numbers by adding two prime numbers together?
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.
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?
Ben has five coins in his pocket. How much money might he have?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
There are lots of different methods to find out what the shapes are worth - how many can you find?
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
Can you substitute numbers for the letters in these sums?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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.
In how many ways can you stack these rods, following the rules?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.