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

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Can you substitute numbers for the letters in these sums?

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?

Find out about Magic Squares in this article written for students. Why are they magic?!

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

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

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

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

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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

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

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

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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

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

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?

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

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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?

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?

What is the best way to shunt these carriages so that each train can continue its journey?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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

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?

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

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

Can you fill in the empty boxes in the grid with the right shape and colour?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Find all the numbers that can be made by adding the dots on two dice.

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

Find out what a "fault-free" rectangle is and try to make some of your own.

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

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.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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.