Rich wrote:
I saw the buried cable problem in one of Gardner's puzzle columns, long long ago.
Thanks very much! A dip into my handy-dandy copy of the MAA's electronic and searchable compendium of the Gardner books turns it up in _Hexaflexagons and Other Mathematical Diversions_, the first column collection with material from SciAm in 1956/7/8. The chapter "Nine More Problems" contains the problem of "The Efficient Electrician," in which there are 11 wires to distinguish. The primary solution Gardner gives is the one which works for any odd number, and he points out the way to change it for any even number as well. He also mentions a variation on the triangle number solution, but one in which you again use information about which other wires each one touches, instead of just the number of them. Using that information, it's just fine if you leave the largest group incomplete, as long as you drop wires from the correct end: with thirteen wires, for example, you group them as rows and columns of * * * * * * * * * * * * * The two different groups of 3 wires are easily distinguished because in only one of them, all wires but one are connected to the group of 2. This seems to still leave open the puzzle construction question. Is there an elegant way to restrict the information you can get out of the system, leaving the sums-of-triangle-numbers method as the best you can do? --Michael -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.