How would I go about solving this 3 Chests problem? How would I go about solving this 3 Chests problem?
I need to either solve or prove that the following riddle is unsolvable.

*

*Chest A contains gold if Chest B contains gold or if Chest C contains gold.


*Chest B contains gold if Chest C contains gold and Chest A contains silver.


*Chest C contains gold if Chest A contains silver.
I've created truth tables based on the 3 statements.
How do I go about either solving it or proving that it can't be solved?

I'm assuming each chest contains either silver or gold.
If C contains gold, then A contains silver (Statement $3$), so B contains gold (Statement $2$).  This contradicts Statement $1$.
If C does not contain gold, then A does not contain silver (Statement $3$), so B does not contain gold (Statement $2$).  Again, (if A contains either silver or gold, this forces A to contain gold), this contradicts Statement $1$.
The combination therefore has no solution.
