Re: Party Puzzle: for your amusement Message #3 Posted by hugh steers on 28 May 2013, 3:00 p.m., in response to message #2 by mike reed
Hello Mike,
Thanks for having a go at the problem. You have correctly highlighted a mistake in my statement of the problem; for an even number of people, it is achievable in n-1 minutes, not n minutes as i originally wrote. So, n=4, gives 3 mins; n=6, gives 5 etc.
However, my tables do show the solutions. They are unfortunately a bit confusing. Taking the first table for n=4
A B C D
B A D C
C D A B
D C B A
The first line indicates A talks to B (min 1), A talks to C (min 2) and A talks to D (min 3) ie 3 mins in total. It does not mean A talks to B whilst C talks to D (although confusingly C does talk to D). The second line is the story according to B, so B talks to A (min 1), B talks to D (min 2), B talks to C (min 3).
You are right that these all look like the same thing repeated over, because they are! The whole table shows the unique solution for 4 people. It might be clearer if i show two solutions for n=6
A B C D E F
B A D E F C
C E A F D B
D F B A C E
E C F B A D
F D E C B A
A B C D E F
B A E C F D
C F A B D E
D E F A C B
E D B F A C
F C D E B A
In the first minute (column 2) C talks to E in the first solution, but talks to F in the second. it's possible to convert the second table into the first showing that these are, in fact, just one solution. But how to easily generate a solution and are they always permutations of each other.
regards,
-- hugh.
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