Ed Pegg Jr., August 17, 2006 Two dimensional surfaces are ideal
for many snake-based puzzles. In 1976, Frank Harary introduced a
new form of tic-tac-toe. As usual, players alternate X's and
O's. For a particular shape and board, player X attempts to make
the shape, while player O prevents the shape. For square boards
and polyominoes, all shapes have been solved except one -- the
Snaky, illustrated below. For thirty years, the Snaky has
remained unsolved. When I saw Dr. Harary in 2004, I asked him
about the Snaky. "Have you solved it?" he asked me, in his warm,
professorial voice. "If you've solved it, I'll put $50 in your
hands right now." I had to tell him that I hadn't solved it. But
perhaps a reader can solve it -- on an 8x8 board, can either X
or O force a win? X wins by making a Snaky in any orientation,
while O wins by reaching a filled board with no Snaky. Figure 1.
The unsolved Snaky. A feature of the Snaky is that it is a strip
polyform. Two squares (the head and tail) each border exactly
one square,