And David, don't forget that the Orientation also counts! Left, Right, or Up should work. That's 3 colors x three sizes x three orientations = 9 possible pieces.
with three slots, that's 9x9x9 = 729 possible koans.
~nupanick (or other appropriate name)
===================
Guvf VF zl jvggl fvtangher.
On Thu, Mar 12, 2009 at 3:50 PM, Christopher Hickman
<tophu@xxxxxxx> wrote:
I'm using this SET rule, I think. I knew it was a good idea to ask here. Thanks everyone!
On Mar 12, 2009, at 3:42 PM, David L. Willson wrote:
I was playing with Zendo Set in my head, and came up with 21 possible koans with the BN, where we use three pyramids with the three usual sizes, and three possible colors of Red, Blue, and Yellow.
(LLL,MMM,SSS)*(RRR,BBB,YYY) = 9 of one size and one color
(LMS)*(RRR,BBB,YYY) = 3 of all sizes and one color
(LLL,MMM,SSS)*(RBY) = 3 of one size and all colors
(LMS)*(RBY,RYB,YBR,YRB,BRY,BYR) = 6 of all sizes and all colors
I'm wondering how many koans ~without~ the BN there are.
Let's see (LLS, LLM, LMM, MMS, LSS, MSS) times 9(?) otherwise valid color combinations... then color combinations would be the same, 6 x 9?
David L. Willson
Trainer, Engineer, Enthusiast
MCT, MCSE, Linux+
tel://720.333.LANS
Freeing people from the tyranny (or whatevery) of Microsofty-ness, one at a time.
----- "Paul Reinerfelt" <paul.reinerfelt@xxxxxxxxx> wrote:
2009/3/12 Nick Lamicela <nupanick@xxxxxxxxx>:
Ooh, I just thought of something! SETs!
AKHTBN iff its colors are either all different or all alike, and it
contains
three pyramids of the same size or one of each size, and the
pyramids are
all in the same orientation or all in different orientations.
White koans:
a red House (treehouse starting setup)
Three upright large pieces of different colors.
Black koans:
two small blue pyramids pointing at a medium yellow between them.
Green large pointing up, Yellow large pointing up, Blue large
pointing
right.
Anyone in your group who's played Set should catch on. A third
example of
each might help, though. Maybe also remove one color so there's
three
possibilities for each value.
Indeed. And a fiendishly difficult koan to others. Very suitable as a
puzzle key in a dungeon.
Good work!
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