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Domino arrangements (Posted on 2006-05-27) Difficulty: 5 of 5
Take the 15 smallest dominoes in a set (double blank through double four.)

In how many ways can they be arranged in a row such that the numbers on consecutive pieces match.

Count the two directions separately.

See The Solution Submitted by Jer    
Rating: 3.6667 (3 votes)

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Hints/Tips No Subject | Comment 2 of 8 |

I believe I can simplify this....

Ok arrange all the dominoes except the doubles in the manner described by the problem.

There are now 4 doubles that could fit in 2 spaces and 1 double that could fit in 3.

Ok, place those 4 doubles in any spots you like and consider moving different numbers of them. If you move none there is 1 possible arrangement of doubles, if you move 1 there are 4 possible arrangements of doubles, if you move 2 there are 6 possible arrangements of doubles, if you move 3 there are 4 possible arrangements of doubles, and if you move all 4 there is 1 possible arrangement of doubles.

This makes 16 possible arrangements for the 4 doubles. Each of these could have the last double in 3 different spaces. So, there are 16x3=48 total arrangements for the doubles. Now you just have to figure out the number of combinations for the ten non-double dominoes and multiply by 48. Hope this helps...

I think my reasoning is correct, but it is 8:00 a.m. and I did not sleep last night...


  Posted by Josh on 2006-05-28 08:30:54
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