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.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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!
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?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
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?
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!
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.
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 sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
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?
There are lots of different methods to find out what the shapes are worth - how many can you find?
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?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
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.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
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.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
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?
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?
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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Investigate the different ways you could split up these rooms so that you have double the number.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
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?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?