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 Arranging numbers in a row (Posted on 2008-11-20)
How many numbers, from 1 to 50 (both included) can you arrange in a row (one of each) so that each one, except the first and the last, is the sum or difference of its two neighbours?

Example: 3, 10, 7, 17, 24, 41.

10 = 3+7, 7 = 17-10, 17 = 24-7, 24 = 41-17.

 See The Solution Submitted by pcbouhid Rating: 2.3333 (3 votes)

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 re(2): Re Charlie's / reply | Comment 9 of 12 |
(In reply to re: Re Charlie's by Charlie)

Yes, Charlie.  I started with eight (since the Fibonacci series was clearly a solution, and when it appeared it would test my code logic).  I just added inner loops one at a time until no solutions.  I suspected that the list would not be too much longer.  My program displayed all solutions for a given length, but not those for shorter lengths; if I added too many loops, and got no hits, I would then have had to remove loops until a solution (preferably unique, other than the reversed pair) appeared.  I saw the number drop from several hundred, to 60 or so, to 6, and then to 2, so it appeared the limit was near.  A recursive solution would be more elegant, but it was easier to code (using COBOL) by just adding one more variable/loop each time, and re-execution (cycles and wall time) was trivial even for the final pass.

 Posted by ed bottemiller on 2008-11-21 11:31:33

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