Thanks for the clarification, Guy. Such claims of "endless" solutions, or "infinite" variations, annoy me too. Also the popular use of "exponential" for things that are not. The YouTube videos suggest that pieces touching only side-to-side may have unreliable contact. So (to light all pieces) we might require vertical contact, so the weight of the upper piece improves electrical contact. I prefer not to require it. A solution counting program would be harder than I first thought, partly due to the difficulty of computing stability when piece(s) are cantilevered. But I will try to compute an upper bound and send it in a separate email. -- Mike ----- Original Message ----- From: "Guy Haworth" <g.haworth@reading.ac.uk> To: <math-fun@mailman.xmission.com> Sent: Sunday, December 28, 2014 1:08 PM Subject: [math-fun] Re Tetris Light Configuration
I was thinking in terms of:
- using only the seven pieces from one instance of the toy, - distinguishing between pieces which are different colours (so the two Zs are different) - NOT 'identifying' particular faces of pieces (so the 'Zs' can be flipped 180 degrees) - touching faces are identically laid over one another, so there are only a finite number of solutions - NOT distinguishing between two arrangements which can be physically translated to each other
The planar constraint (required to light all pieces) only applies if they are all required to light up.
The question of the number of arrangements is rather prompted by the 'endless' claim on the packaging. :-)
Guy
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