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Domino Chain (Posted on 2004-02-11) Difficulty: 4 of 5
Two dominoes are picked at random from a standard set of double-sixes. Such a set contains all the possible combinations of two numbers of pips that are possible from zero to six. That includes all 7x6/2=21 combinations of two different numbers plus all seven doubles from double zero to double six.

You look at only one of the two numbers on each domino, choosing at random which end to look at. You see that the number you look at on the first domino is 1. The number you see on the second domino is 2 (of course represented as pips).

What is the probability that you will be able to use these two dominoes as the ends of a chain of dominoes using all 28 in the set, linked in the usual fashion of requiring a match between the two adjoining numbers of two touching dominoes?

Remember, the numbers you looked at need not be the end numbers--one or the other of the still-hidden numbers might be positioned at the actual end(s) of the chain.

See The Solution Submitted by Charlie    
Rating: 3.7143 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(4): solution :-) | Comment 10 of 19 |
(In reply to re(3): solution :-) by SilverKnight)

Your paraphrase is not as specific in the method of choosing two dominos and the ends to look at. Ask which is a more likely domino to choose: for example, the 1-5 or the 1-1. Also determine at random an end to look at.
  Posted by Charlie on 2004-02-12 08:39:37

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