perplexus.info :: Probability : Domino Polygons

Domino Polygons (Posted on 2011-03-14)

Randomly draw three from a standard set of 28 Double Six Dominoes.

What is the probability they can be arranged in a triangle with each end touching another end with an equal number of spots?
For example: [1|3][3|0][0|1] can form such a triangle.
(Note: this triangle is not a legal configuration in an actual game of dominoes.)

Randomly draw four dominoes instead.
What is the probability of being able to form a square in the same fashion?

How about 5? 6? 27? 26?

There doesn't seem to be a general formula. Is there?

No Solution Yet Submitted by Jer

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27? 26? (spoiler)

| Comment 2 of 5 |

27 randomly drawn can form a 27-gon only if the undrawn 28th is a double. Probability = 7/28 =1/4.

26 randomly drawn can form a 26-gon only if the undrawn 27th and 28th are both doubles. Probability = 7/28 * 6/27 = 1/18

Posted by Steve Herman on 2011-03-14 23:16:50

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