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?

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

How many different symmetrical shapes can you make by shading triangles or squares?

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.

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?

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.

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

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

Use the clues about the symmetrical properties of these letters to place them on the grid.

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.?

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

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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

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?

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?

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?

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

This activity investigates how you might make squares and pentominoes from Polydron.

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

An activity making various patterns with 2 x 1 rectangular tiles.

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

In how many ways can you stack these rods, following the rules?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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?

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

Design an arrangement of display boards in the school hall which fits the requirements of different people.

The pages of my calendar have got mixed up. Can you sort them out?

In this matching game, you have to decide how long different events take.

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?

These practical challenges are all about making a 'tray' and covering it with paper.

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Four small numbers give the clue to the contents of the four surrounding cells.

This dice train has been made using specific rules. How many different trains can you make?

Use the differences to find the solution to this Sudoku.

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This Sudoku, based on differences. Using the one clue number can you find the solution?