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?

Helena