Date: Jan 27, 1999 3:02 PM
Author: Helena Verrill
Subject: coins problem

a little while ago, someone asked the following:

if you have 12 coins, one of which is either
heavier or lighter than the others, the others all
being the same weight, how can you determine which
one it it, and whether it's heavier or lighter, in
three weighings.

Well, I did't think about this problem until last
weekend when I heard it for a second time.
Anyway, it's not too hard to solve, but how about
what is the minumum number of weighings that you
need to determine which is the odd one, and whether
it's heavy or light, from n coins?
Eg, you can do 3 coins in 2 weighings,
12 coins in 3, 38 coins in 4 weighings -
I'd rather ask for what is the sequence a_n
so that a_n is the maximum number of coins such
that the odd one can be found (and said to be heavier
or lighter). I'd guess this starts 3,12,38...
but I can't find this sequence in Sloanes integer
sequences, so presumably that means 38 is not the
max you can do in 4 weighings... Anyone else tried?