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?
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?
Number problems at primary level that require careful consideration.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Can you substitute numbers for the letters in these sums?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
This task follows on from Build it Up and takes the ideas into three dimensions!
You have 5 darts and your target score is 44. How many different ways could you score 44?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
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.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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. . . .
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Find out what a "fault-free" rectangle is and try to make some of your own.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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 replace the letters with numbers? Is there only one solution in each case?
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
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?
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.
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
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 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!
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?