Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.

A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

A game for 2 players with similaritlies to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.

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 Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

There are lots of different methods to find out what the shapes are worth - how many can you find?

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

An ordinary set of dominoes can be laid out as a 7 by 4 magic rectangle in which all the spots in all the columns add to 24, while those in the rows add to 42. Try it! Now try the magic square...

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

Using the interactivity, can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Everthing you have always wanted to do with dominoes! Some of these games are good for practising your mental calculation skills, and some are good for your reasoning skills.

A game for 2 players. Take turns to place a counter so that it occupies one of the lowest possible positions in the grid. The first player to complete a line of 4 wins.

Can you work out how to win this game of Nim? Does it matter if you go first or second?

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

A game that demands a logical approach using systematic working to deduce a winning strategy

Can you mentally fit the 7 SOMA pieces together to make a cube? Can you do it in more than one way?

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Use these four dominoes to make a square that has the same number of dots on each side.

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

How many moves does it take to swap over some red and blue frogs? Do you have a method?

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

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.

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Is it possible to use all 28 dominoes arranging them in squares of four? What patterns can you see in the solution(s)?

Using the 8 dominoes make a square where each of the columns and rows adds up to 8

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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?

In the ancient city of Atlantis a solid rectangular object called a Zin was built in honour of the goddess Tina. Your task is to determine on which day of the week the obelisk was completed.

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

A game in which players take it in turns to choose a number. Can you block your opponent?