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?
 A: Assume your translation is correct, and you can just build a truth table of the conjunction of all your above 3 clauses to see if it's satisfiable or not.
$$A~~|B~~|C~~|~~(A↔(B∨C))∧(B↔(C∧(¬A)))∧(C↔(¬A))$$
And use some online tool like this you can quickly see its negation is a tautology, thus this puzzle as interpreted by your above logic translation is unsolvable since it's a negation of a tautology (aka a contradiction)...
A: There is no solution to this problem.
If $A$ contains gold then either chest $B$ or $C$ contain gold. $C$ contains gold if and only if $A$ contains silver. Therefore $C$ does not contain gold and so, $B$ must contain gold which means $C$ contains gold which is a contradiction.
If $A$ contains silver then $C$ contains gold which means $A$ contains gold. This is also a contradiction.
Therefore, there is no solution.
A: 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.
