Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?

A game for two players based on a game from the Somali people of Africa. The first player to pick all the other's 'pumpkins' is the winner.

A game for 2 people. Take turns joining two dots, until your opponent is unable to move.

Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

This game for two, was played in ancient Egypt as far back as 1400 BC. The game was taken by the Moors to Spain, where it is mentioned in 13th century manuscripts, and the Spanish name Alquerque. . . .

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .

An ancient game for two from Egypt. You'll need twelve distinctive 'stones' each to play. You could chalk out the board on the ground - do ask permission first.

This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .

Can you fit the tangram pieces into the outline of the house?

A huge wheel is rolling past your window. What do you see?

Can you fit the tangram pieces into the outlines of the telescope and microscope?

Can you fit the tangram pieces into the outline of Mah Ling?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outlines of the people?

Can you fit the tangram pieces into the outline of Little Fung at the table?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Can you fit the tangram pieces into the outline of Little Ming?

Can you fit the tangram pieces into the silhouette of the junk?

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

Can you fit the tangram pieces into the outline of the child walking home from school?

This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

Can you fit the tangram pieces into the outline of the sports car?

Can you fit the tangram pieces into the outline of the telephone?

Can you fit the tangram pieces into the outlines of the numbers?

Can you fit the tangram pieces into the outline of the brazier for roasting chestnuts?

Can you fit the tangram pieces into the outline of the butterfly?

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

Can you fit the tangram pieces into the outline of the playing piece?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

Can you fit the tangram pieces into the outline of the clock?

Can you fit the tangram pieces into the outline of this teacup?

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Can you fit the tangram pieces into the outline of the candle?

I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Can you fit the tangram pieces into the outlines of Mah Ling and Chi Wing?

A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .