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?

Number problems at primary level that require careful consideration.

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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?

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?

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

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

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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. . . .

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

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

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.

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

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!

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

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?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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?

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.

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

What happens when you round these three-digit numbers to the nearest 100?

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

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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

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?

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

Can you find all the ways to get 15 at the top of this triangle of numbers?

Can you use the information to find out which cards I have used?

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

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?

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?