This is the classic "The Reve's Puzzle" as
described by Henry Dudeney in "The
Canterbury Puzzles". In Dudeney's
original story, the Reve -- one of
Chaucer's pilgrims -- set up four stools
and placed eight cheeses of differing
sizes on one of the stools. He then
challenged the other pilgrims to move the
cheeses to another stool in the least
number of moves possible. The cheeses had
to be moved one at a time and no cheese
could be placed on a cheese that was
smaller. After moving eight cheeses, a
pilgrim had to move nine cheeses, and then
ten, and so on until finally moving 21.
The Reve promised to give a pilgrim who
was able to move 21 cheeses in the least
number of moves "a draught of the best
that our good host can provide."

This application implements Dudeney's
Puzzle.

To move a cheese, the player simply
touches in a region near a stack of
cheeses. The top cheese on that stack
will move to the player's finger. Then
the player just drops that cheese on
another stool. If the move is not
allowed, the cheese will return to the
stool where it started.

The moves are counted. The goal is to
move all the cheeses to another stool in
the minimum number of moves possible. If
the player makes an inadvertent move, it
can be taken back as long as nothing else
is done in the meantime.

This puzzle has two modes, a "Practice"
mode and a "Puzzle" mode.

In Practice mode:

- The player can practice moving from
eight through 21 cheeses and can start
over again at any time.
- The player can ask to be shown how to
move the cheeses.

When the puzzle shows the player how to
move the cheeses, it will move them in
the least number of moves possible but
will not always move them the same way.
The animation runs faster when there are
more cheeses to be moved.

In Puzzle mode:

- The player has to move eight cheeses in
the least number of moves possible,
and then move nine, and then move ten,
and so on until finally moving 21
cheeses in the least number of moves
possible.
- The puzzle keeps track of the number of
moves and the elapsed time.
- The player can start over at the
current number of cheeses at any time,
and can begin again with eight cheeses
as well.
- The player can stop the game at any
time and resume from that point later.
If the player exits Puzzle mode and
goes to Practice mode, the clock stops
and starts again when Puzzle mode is
reentered.
- When the player has succeeded in moving
all the cheeses from eight through 21,
the puzzle will allow the player to
send his or her name and the time
that it took to be posted on the
puzzle's web page.

It is fairly easy -- but not trivial -- to
move eight cheeses in 33 moves, but it
becomes more and more challenging as the
number of cheeses increases. It takes at
least 33 moves to move eight cheeses but
takes 321 moves to move 21 cheeses, and
that's if no mistakes are made!

The puzzle is similar to the Towers of
Hanoi puzzle, but due to having four
stools, it takes many fewer moves. At the
same time, this puzzle is significantly
more challenging than the Towers of
Hanoi. It is an open problem in
mathematics to determine the minimum
number of moves for all numbers of cheeses.

More information about this puzzle is at
http://www.revespuzzle.com

Comments and suggestions are welcome.
Please send them to
TheRevesPuzzle@gmail.com

Here's one comment that we received that
we particularly appreciated:

"Absolutely LOVE the animation. ... a
brilliant implementation." David Mark