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.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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 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 task follows on from Build it Up and takes the ideas into three dimensions!
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.
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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!
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 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!
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 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?
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?
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
What could the half time scores have been in these Olympic hockey matches?
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.
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
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?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
How many trapeziums, of various sizes, are hidden in this picture?
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?
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.
The Zargoes use almost the same alphabet as English. What does this birthday message say?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
These activities lend themselves to systematic working in the sense that it helps if you 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.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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?