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.  

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