Can you substitute numbers for the letters in these sums?

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 require careful consideration.

Can you replace the letters with numbers? Is there only one solution in each case?

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?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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?

Have a go at balancing this equation. Can you find different ways of doing it?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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.

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!

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Given the products of adjacent cells, can you complete this Sudoku?

Can you work out some different ways to balance this equation?

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.

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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!

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?

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?

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?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

This dice train has been made using specific rules. How many different trains can you make?

There are lots of different methods to find out what the shapes are worth - how many can you find?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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?

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?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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.

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

Can you make square numbers by adding two prime numbers together?

This task follows on from Build it Up and takes the ideas into three dimensions!

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?