Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

This challenge is about finding the difference between numbers which have the same tens digit.

What two-digit numbers can you make with these two dice? What can't you make?

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?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

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

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

An investigation that gives you the opportunity to make and justify predictions.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

Can you find out in which order the children are standing in this line?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

The Zargoes use almost the same alphabet as English. What does this birthday message say?

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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?

What could the half time scores have been in these Olympic hockey matches?

My coat has three buttons. How many ways can you find to do up all the buttons?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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

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

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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?

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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?

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?

Can you find the chosen number from the grid using the clues?

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