This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
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.
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
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?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
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 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?
How many possible necklaces can you find? And how do you know you've found them all?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?
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?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Investigate the different ways you could split up these rooms so that you have double the number.
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?
Can you use this information to work out Charlie's house number?
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
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?
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
You have 5 darts and your target score is 44. How many different ways could you score 44?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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.
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.