Good question. Should be not too hard to program an enumeration. But a tad more specification is needed. (Else, upper bound as a function of, say, number of pieces.) The "face to face" requirement is critical, because pieces will light even if they are translated a bit or tilted, just so long as their front and back metal pieces touch. Infinite solutions without grid alignment. Need to restrict to (say) 1 set, 1 each of the 7 tetrominoes. Apparently multiple sets can be stacked and will light; the maker's warning is only because tall structures may fall over catastrophiclly. The mirror pair pieces (2 L's, 2 Z's) can be turned over and used in constructions that light OK. So, need to specify whether this is allowed in the counting of configurations. If turning over the L's or Z's is allowed, note they still have distinct colors. So, need to say whether (after flipping one) the pieces are distinct due to color, or not. I think condition (B), that all pieces light up, is ensured if every piece touches another piece. Except for poor electrical contact, touching should ensure power, thus light. The I is the only piece directly powered by the AC adapter. Solutions are essentially planar and standing on a table top. Need to say whether mirror pair solutions count as distinct. (Does every solution have a vertical axis mirror, or are any self-mirror? Are any self-mirror across horizontal axis?) I suggest using all of, and only, 1 set; no piece flipping; mirror image solution pairs count as one solution. My comments on the design: I is blue; one L is pink, one orange; O is yellow; T is purple; one Z is green, one red. It looks like they must not be placed non-planar, because a piece in the third dimension would short out the power, which I assume is on the front and back metal edges. This gadget has been around for a couple years, and seems to get rave reviews. Some online places (e.g., Think Geek) are sold out. About $40 US; cheaper knock-offs apparently exist. -- Mike ----- Original Message ----- From: "Guy Haworth" <g.haworth@reading.ac.uk> To: <math-fun@mailman.xmission.com> Sent: Friday, December 26, 2014 7:03 AM Subject: [math-fun] Tetris Light configurations
So ... my wife buys Tetris Lights for some children ... http://www.firebox.com/product/5339/Tetris-Light ... made of seven tetrominoes.
What is an upper bound on the number of configurations in which the components are face-to-face touching another component on at least one face so that:
- all components will (A) stand stationery and (B) light up, or - one or both of conditions 'A' and 'B' are ignored.
Guy
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