In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Number problems at primary level to work on with others.
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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.
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.
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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?
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Here is a chance to play a version of the classic Countdown Game.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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.
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!
If you have only four weights, where could you place them in order to balance this equaliser?
Number problems at primary level that require careful consideration.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
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 problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
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?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Can you substitute numbers for the letters in these sums?
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.