What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
The Zargoes use almost the same alphabet as English. What does this birthday message say?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
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?
This article for primary teachers suggests ways in which to help children become better at working systematically.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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.
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.
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.
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?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
In how many ways can you stack these rods, following the rules?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
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?
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?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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?
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?
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.?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
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?
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.
What is the best way to shunt these carriages so that each train can continue its journey?
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you use this information to work out Charlie's house number?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
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?