Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.
Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.
In this matching game, you have to decide how long different events take.
The pages of my calendar have got mixed up. Can you sort them out?
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
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.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
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?
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?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
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.
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, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
An investigation that gives you the opportunity to make and justify predictions.
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
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.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
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?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
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?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.