Trouble in Triplicate
For all legmen who hate to commute.
"Welcome to Ordered Triplet, America's favorite abstract-symbols game show! Who are our lucky contestants today, Pat?"
"Well, Vanna, at the top left we have Brian from Roxy Music, in the center Keanu Reeves in a trenchcoat (how appropriate!), and at the bottom right, Eli from Little Orphan Annie. Just look at them all dance around!"
"Yes, I love how they're holding up their giant foam fingers and chanting."
"Then in the middle left, Mr. Mostel from The Producers; bottom left, Jennifer Hewitt from Ghost Whisperer; and bottom middle, an unhatched anserine waterfowl."
"They seem to be saying nothing, Pat."
"Don't let that fool you, Vanna; when it comes to playing, they've all got plenty of zip. Finally, we have Gray Davis top right, Brad Paisley middle right, and Thelonious Sphere Monk top middle -- all fine examples of the sort of quality players we like to have here.
"Great! Now, for the viewer at home: this game is just like a certain popular card game, except for two exciting innovations I have introduced. First, to keep things simple, each card has only one symbol on it."
"So there are only 27 distinct cards?"
"Right, Pat. Second, instead of attempting to produce the identity element in the direct sum of four copies of the cyclic three-group (taking the possible values of each quality as 0, 1, and 2, mod 3), you are instead trying to produce the identity element in . . . yes, Pat?"
"Does that mean that <red solid squiggle, red hollow diamond, red striped oval> is not a correct triple? Or <red solid squiggle, green hollow oval, blue striped diamond>?"
"No, both of those still work. But, for example, <red hollow diamond, red solid squiggle, red striped oval> is not correct, while <red hollow diamond, red solid squiggle, green striped oval> is."
"So that's why the cards in the set backdrop aren't all the same color?"
"Exactly, Pat. And now -- let's play!"