a maze is defined as a
branching path with no loops, no corner-wise connections
and all connections should be a single unit width.

an elegant maze covers the
area such that no spaces are more than a single unit in
width.

Problem 1:
What is the largest area in which an elegant maze can be
built with a set of 12 pentominoes?

Hover over an image to see a
solution.

17 x 7 solution (not the largest
possible solution)

Problem2:
What is the longest “correct” path which can be formed in an
elegant maze, ignoring dead ends?

path length = 37 (not the longest
possible solution)

In a set of mono-through-pentominoes, only the P pentomino and square tetromino
contain a 2x2 block.

Problem 3:
Using such a set, what is the longest “correct” path which
can be formed in an elegant maze, starting at the "P"
pentomino and ending at the square tetromino?

path length = 37 (not the longest
possible solution)

Seven of the pieces contain squares
which cannot form part of the path. These pieces are shown
below with one possible longest path highlighted. So the
maximum possible path length for mazes is the total number
of squares minus these eliminations. For the pentominoes
this gives 60 - 6 = 54, and for the mono-through-pentominoes
it is 89 - 8 = 81.