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

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?

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?

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

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

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.

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

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

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

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

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?

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.?

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

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.

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Can you find all the different ways of lining up these Cuisenaire rods?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using 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?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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?

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?

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.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Two sudokus in one. Challenge yourself to make the necessary connections.

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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?

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

How many different triangles can you make on a circular pegboard that has nine pegs?

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?

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

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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.

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?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?