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

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

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 numbers to the nearest whole number?

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

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?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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?

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?

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

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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

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

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?

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

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

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

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

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

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?

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?

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.

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

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?

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

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

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

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?

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

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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

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

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

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

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

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