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It can be readily generalised to d dimensions. Imagine Lego in 10D

BTW, in William Gibson's Pattern Recognition, he says about its two protagonists "Their boy-girl Lego doesn't click." (to explain why they are just friends, not in a romantic relationship). I've never actually understood what that meant. Do you know?

Statistics: Posted by katastrofa — February 14th, 2017, 6:56 pm

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House rules suffer from Godel's Syndrome -- they are either incomplete or inconsistent which leads to discord!

Methinks Mrs Traden4Alpha and Mrs Outrun would assert that the answer to this brainteaser is 1. The only acceptable solution is the block-aligned-with-block configuration because that minimizes space and gets the damned legos off the carpet!

Statistics: Posted by Traden4Alpha — February 13th, 2017, 2:47 pm

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With the offset-coordinate method, one coordinate ranges over the full left-to-right range whereas the other coordinate ranges over half the top-to-bottom range except for the offset that centers to top brick over the bottom brick in which left-to-right is only half the range, too. I'd initially made an error in that half-rangecase and written 3x3+1 = 10 in my post, caught the error, corrected to 3x3+2 but forgot to recalculate. (It's the curse of procedural programming!)

The coloration of the solution seems strange in that there's other block-pairs that don't have left-right types. All of the "T" configurations are "unique" in this way, too.

Statistics: Posted by Traden4Alpha — February 13th, 2017, 1:12 pm

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Statistics: Posted by outrun — February 13th, 2017, 11:15 am

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The analyzer would assign rotationally congruent block-pairs to the same equivalence class and left-handed/right-handed assemblies to different classes. But what does it do if it has one block-pair with a 37° swivel angle and another block-pair with a 38° swivel angle? They are not congruent in their snapped-together configuration.

If we ignore the swivel issue, the one answer can be constructed using relative coordinates method (with culling for some symmetries). For parallel-oriented blocks, I get 3x3+2 = 10 configurations. For perpendicular-oriented blocks, I get 5x2+3 = 13 configurations. SO the total seems to be 23.

---EDIT---

For parallel-oriented blocks, I get 3x3+2 =

Statistics: Posted by Traden4Alpha — February 13th, 2017, 1:43 am

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1) There is a difference left- and handedness.

2) DOF is *property* of a specific solution. Some solutions can swivel, others can't. So if't more about counting the number of ways you can snap them together?

Statistics: Posted by outrun — February 12th, 2017, 9:02 pm

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It seems that the feasible sets of connections would involve: 1, 2, 3, 4, 6, 8 overlapping bumps.

There are some open questions of what constitutes a "different way":

1. Chirality: If one snaps the top block on to the bottom one to form an "L", there's the question of whether a right-handed L is "different" from a left-handed L.

2. Swivel DOF: If the blocks are connected by only 1 bump, the blocks can swivel through a range of angles which might be counted as 1 way or an infinite number of ways.

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There may be a quick way to calculate the number from the range of relative (X,Y) coordinates of the top block's corner WRT the bottom block with two cases for parallel vs. perpendicular relative orientation and then minus some cases that are congruent under rotation.

Statistics: Posted by Traden4Alpha — February 12th, 2017, 7:04 pm

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Since women to men ration in Iranian team was 3:1 and in Israeli team was 1:8, it's easy to see that tampering with these matches could affect Hou's draws. Anyway, as calculated above by outrun and I, the result is highly unlikely (H0 is that the draws are random).

I had a colleague who was an Olympic swimmer. She told me that everyone knew that eliminations were rigged or bought. It looks like chess tournaments are the same.

I've tried to explain in this thread several times now why Hou was wrong and her pairings weren't rigged. I'm fairly knowledgeable about the subject matter and know where to look and who to believe for info about this specific case. If you continue to assert "it's rigged" you just look like Amin and his significant breakthroughs. The Israel/Iran pairings were too low down the field to affect Hou who is a 2600 GM. Some rigging does happen in chess, particularly where titles or norms are concerned, but not in Hou's case.

Statistics: Posted by MattF — February 7th, 2017, 3:01 pm

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I had a colleague who was an Olympic swimmer. She told me that everyone knew that eliminations were rigged or bought. It looks like chess tournaments are the same.

Statistics: Posted by katastrofa — February 7th, 2017, 2:32 pm

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