Determine which is the chest which contains "100 gold coins", you are allowed to randomly pick a coin from any chest?

Question

In front of you are 3 chests:
Chest A has been labelled with "100 gold coins",
Chest B has been labelled with "50 gold and 50 silver coins",
Chest C has been labelled with "100 silver coins".

You are told that all of the labels are incorrectly placed, as they describe the contents of another chest. To help you determine which is the chest which contains "100 gold coins", you are allowed to randomly pick a coin from any chest,

Which chest should you pick a coin from?

Answer 1

You should pick a coin from chest B. This coin you pick (either gold or silver) will be the entire content of the chest. If it is gold, chest B is 100 gold coins, if it is silver, chest C will contain the 100 gold coins.

Let say you pick gold. As chest B cannot contain silver and gold, it must contain only gold.
Let say you pick silver. As chest B cannot contain silver and gold, it must contain only silver. Chest A cannot contain only gold and as chest B contains only silver, chest A must contain silver and gold. That leaves chest C for only gold.