Floyd Johnson on 15 Sep 2011 20:22:08 -0700 |
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Re: [Philadelphia-pm] 378,000 milkshakes |
On Thu, 2011-09-15 at 19:01 -0400, Mark Jason Dominus wrote: > > We attempted to figure out how they had arrived at that number. > > That is a funny synchronicity. Just last night I was trying to think > of a good algorithm for solving the following problem: given a > positive integer M, find n > 0 and k > 1 such that M = n choose k = > n!/k!(n-k)!, or determine that no such n and k exist. > I'll raise you one on "synchronicity" by adding "esoterica": En route home this afternoon, on a question of how technology has progressed, I bumped into the topic of "permutations" (even twenty years ago, combinatorics was painful)-I knew factorials were involved in working such "n choose k" matters, but you have just filled the gap in my memory. I was trying to guess what, for an old tabletop game called "Electronic Detective", the processor and storage matters (if even applicable) might have looked like. I think the box claimed "over 100,000 possible cases". What I recall is: -20 characters total to be potentially questioned, exactly one being the victim, exactly one other the culprit. Mathwise, this is "20 choose 2". -Six locations, exactly one is the crime scene, the other five assigned to the 19 surviving characters as where each fled to when the shots rang out. A more-modern version might make use of the possibility of one "potential witness/suspect" having seen another were the two assigned the same location by the "case generator". "6 choose 1" for the crime scene (three bits); "19 choose 5" for where everyone else went; the culprit is, as the included soundsheet explains, "too smart to return to the scene of the crime". -Two possible weapons. This would mean what we call a Boolean. I think it also might have stored the number of players and one other piece of user-supplied info punched in just after it finished "booting". Those, being two 0 through 9 digits, would most sanely be crammed into a single 0-99 value, translating to seven bits. I can't seem to bring myself to grind out the factorials, but I have a curious feeling that any RAM in the thing might have been less than a quarter-K (256 bytes). In theory, someone with the marbles for combinatorics (make of that what you will) might be able to reverse-engineer that ancient Ideal-branded bit of electronics. _______________________________________________ Philadelphia-pm mailing list Philadelphia-pm@pm.org http://mail.pm.org/mailman/listinfo/philadelphia-pm