Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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.

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

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

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?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

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?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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.

Number problems at primary level that require careful consideration.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

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

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

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

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

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

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

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

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

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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?

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

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

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?