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.
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?
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?
Did you know that ancient traditional mazes often tell a story?
One such story is ancient Celtic tale The Raid of Fraech's Cattle.
The story tells how the hero Conall Cernach helps to rescue
Fraech's magic cows which have been stolen by some warriors. The
valuable cows are being kept with other treasures inside a mountain
fortress, guarded by a mighty serpent. A helpful milk maid lets
Conall into the fortress at night. It appears that the hero and the
serpent may have met before because, instead of attacking Conall,
the snake darts into his waist belt. After releasing the cows and
taking some treasure, Conall lets the snake out of his belt without
harming it and leaves the fortress.
Remembering this story helps to draw the basic maze pattern: The
fortress of the mighty serpent of Val Camonica. To draw it, you
will need a pencil and an eraser.
First draw the stick figure for Conall, wearing his horned hat.
Then draw a spiral, starting over his head, through his middle,
around twice, stopping just before his legs, and close off the
spiral. This is the long serpent passing through his waist belt.
(Don't draw the coils of the snake too close together).
Now erase a the bottom piece of the snake that crosses the
figure, and erase the legs. (Conall slips the snake out of his belt
and leaves the fortress).
Just two inside walls to draw now. First, start at the beginning
of the snake. Go down then up and over the top of the hat. Start a
new line at the very top of the hat. Go down then, up over the line
you just drew. Carefully erase the horns from the hat and the
fortress is complete.
This is a traditional Camonica Valley Maze. This and other mazes
can be found in the book Celtic Design: Maze Patterns by Aidan
For more about mazes why not look at the "
More on Mazes " article.