You have eight bags, each of them containing 48 coins.

Five of these bags contain only true coins, the rest of them contain fake coins. Fake coins weigh 1 gram less than the real coins.

You do not know what bags have fake coins and what bags have real coins. You do not know also, besides that it is an integer value, the weight of the real coins.

You can use a digital or analog reading scale with precision up to 1 gram.

Making only one weighing and using the minimum number of coins, how can you find the bags containing the fake coins?

The answer I found was 1, 2, 3, 5, 8, 14, 25, 45 coins from the eight bags. 

At first I thought that one bag could be set to the side, but it did not leave differing results for all measurements.

I used a spreadsheet and worked from 4 sacks all the way to 8.

Looking at the OLEIS this sequence is A36241 which is roughly: a list of numbers where any three will sum to a different total.

1,2,3,4,8,14,25,45,82,140 would be needed for three bags of fake coins out of 10 total.

Posted by Leming on 2008-10-23 19:34:50