Um.. Yeah.. Off by one. I gave how many changes of orderings there are, so add one for the total number of orderings. DOH! ;-) On Mar 27, 2016 04:01, "Gareth McCaughan" <gareth.mccaughan@pobox.com> wrote:
On 27/03/2016 03:38, William R. Somsky wrote:
If done w/ sufficient resolution, and barring a measure-zero set of
coincidences, your procedure w/ N dead presidents should result in N(N-1)/2 different orderings. And nice question -- I solved it while driving in the car to get dinner. :-)
I think you have an off-by-one error.
N=1: N(N-1)/2 = 0, but obviously there's one ordering.
N=2: N(N-1)/2 = 1. Suppose we have A (born 0, died 1) and B (born -1, died 2). Then just "born" and "died" already give us both possible orderings.
N=3: N(N-1)/2 = 3. Suppose we have A(0..0), B (1..2) and C(0..3). Then, if h is very small and positive, we have the following orderings: - b + h(d-b): A < C < B - b - h(d-b): C < A < B - b + 1(d-b): A < B < C - b - 9(d-b): C < B < A
(You get one *change* in ordering per "line joining two of the points", not one *ordering*.)
-- g
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