On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
Annie and Ben are playing a game with a calculator. What was Annie's secret number?
This challenge is about finding the difference between numbers which have the same tens digit.
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .
Fill in the numbers to make the sum of each row, column and diagonal equal to 15.
Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
There were 22 legs creeping across the web. How many flies? How many spiders?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?
Use the information to work out how many gifts there are in each pile.
Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?
Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
Can you find 2 butterflies to go on each flower so that the numbers on each pair of butterflies adds to the same number as the one on the flower?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
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.
Number problems at primary level that require careful consideration.
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Can you make square numbers by adding two prime numbers together?
How would you count the number of fingers in these pictures?
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?
If the answer's 2010, what could the question be?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
Number problems at primary level to work on with others.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Number problems at primary level that may require resilience.
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Find all the numbers that can be made by adding the dots on two dice.
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?