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:: The Five Bags of Coins::

You are given 5 bags containing 100 coins each. The bags can contain coins of 3 different types that look identical. The first type weighs 9 grams, the second type 10 and the third type 11 grams. Each bag contains coins of equal weight but you do not know how many of the 5 bags are of the different types. (i.e. all 5 bags might well contain 9 gram coins as far as you are concerned). You are given a huge digital balance. How many times do you need to use the balance to clearly dertermine the type of coin contained in each bag?

Hint: Do the Copper/Gold coin problem first.

Answer:

It can be done in one measurment only. The way to reason here is to first label the bags 1 to 5 then extract a certain number of coins from each bag in such a way that the total sum of the weights of the coins extracted corresponds to one and only one possible configuration or arrangement of the weights for each bag. If there were just 2 types of allowed coins then the number to extract from each bag would be {1,2,4,8,16} ...(i.e. powers of 2). In our case with three types of coins we need to extract {1,3,9,27,81} coins...(i.e. powers of 3). No wonder each bag has to contain more than 81 coins ... 100 is a good choice!