During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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.

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

Try this matching game which will help you recognise different ways of saying the same time interval.

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

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?

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?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

A challenging activity focusing on finding all possible ways of stacking rods.

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?

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?

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?

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?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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

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?

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

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

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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

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?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

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?

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

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?

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

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?

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

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

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?

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

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

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?

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.

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

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

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?