[Edu] Making Games

[Don Sheldon]

On 8/17/06, Kate Jones <kate at gamepuzzles.com> wrote:
> If you lay them out in groups, you'll find that every card has four
> different images, in 5 pairs, where each pair omits a different one of the 5
> images of the set; and each image occurs the same number of times, but with
> 4 on the right and 4 on the left. So the cards do constitute a set of all
> different combinations, though not in every possible different relative
> position. Each individual image can be seen as occurring the same number of
> times in all possible different positions on the 4 corners. Evidently an
> intriguing neighboring protocol was used:  where they occur on the same
> card, stars and fish are always together; flames and flowers are always
> together; ditto rainbow and flame. With everything in the deck being in
> groups of 5 or 10 or 15, this arrangement of the 4-panel set was the most
> effective way to have all different combinations on just 10 cards. Quite a
> brilliant solution, wouldn't you say? If I've missed part of the formula,
> I'd love for Andy to explain it.

By my quick scribbles... there are 60 possible 4 panel cards.
Remember that if you have

Air Fire
Earth Water

it's the same as

Water Earth
Fire Air

because you can just turn it around.  That means there are 5!/2 =
5*4*3 = 60.  Yeah, 60.  (pick the missing element (5 options), pick
the "first" element on the card (4 options left), then the second (3
left), third (two left) and fourth (only 1 option left there), and
divide by two because of the above mentioned rotation duplication.)

Hrm... now I'm gonna go dig out my Aquarius deck, hold on.

<time passes>

Yeah, I don't see any over-riding pattern that hasn't already been
mentioned.  I'm stumped.  I'm willing to say it's pretty much random,
except that the transformations between cards of the same element make
up varies distinctly from group to group.  Some are just 90 degree
rotations.  Some are mirror images, some are, well, something else
that I don't have a simple explanation for, but you get the idea.

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  hmmm