Question

You have three chests in front of you. The first chest is labeled "GOLD", the second is labeled "SILVER" and the third is labeled "GOLD OR SILVER". You have been told that all the labels are on the wrong chests and that one chest contains gold coins, one contains silver coins and one contains bronze coins. How many chests do you need to open to deduce which label goes on which chest?

• A. 0
• B. 1
• C. 2
• D. Cannot deduce

Hint:

Start with the chest labeled "GOLD OR SILVER". Since every label is wrong, this chest cannot hold gold or silver, so its true content is forced without opening anything.

Answer 1

The Correct Option is A

Step 1: List what each wrong label forbids.
Label on chest 1 is "GOLD", so chest 1 $\neq$ gold.
Label on chest 2 is "SILVER", so chest 2 $\neq$ silver.
Label on chest 3 is "GOLD OR SILVER", so chest 3 $\neq$ gold and chest 3 $\neq$ silver.

Step 2: Narrow chest 3 first, since it has two restrictions.
Chest 3 cannot be gold and cannot be silver, and the only three possible contents are gold, silver and bronze. That leaves exactly one option for chest 3: bronze.

Step 3: Fill in the rest by elimination.
Bronze is now used up by chest 3, so chest 1 and chest 2 must split gold and silver between them.
Chest 1 cannot be gold, so chest 1 must be silver, which leaves chest 2 as gold, and this also agrees with chest 2's own restriction, since chest 2 $\neq$ silver, and gold fits fine.

Step 4: Check the whole assignment is self-consistent.
Chest 1 = silver (label said gold, wrong, correct), chest 2 = gold (label said silver, wrong, correct), chest 3 = bronze (label said gold or silver, wrong, correct). Every condition of the puzzle checks out with no contradiction, and this is the only assignment that works.

Final Answer:
Since one unique solution falls out just from the fact that all three labels are wrong, no chest needs to be physically opened. \[ \boxed{0} \]