Spoiler Alert: Bard punts when pressed for the correct response.

The Prompt

Assume you are the Queen of a Land and your treasury has 4 gold coins, one of which is known to be authentic and one that is known to be fake. How many times do you have to measure your coins to determine the fake? Provide your logical proof.

ChatGPT-4’s Response

In this scenario, you can find out which coin is fake in just one measurement, assuming that you have a balance scale available. Here’s how:

1. Take the coin that you know is authentic and one of the unknown coins and put them on one side of the balance. Take the remaining two coins and put them on the other side of the balance.

2. Now, there are two possible outcomes:

a. If the balance is equal, then the fake coin is the one left out during the measurement (since it is lighter or heavier than the rest). In this case, you’ve used the balance only once to find out the fake coin.

b. If the balance is not equal, then the fake coin is one of the two on the side that is lighter or heavier (depending on what characteristic the fake coin has). Since the coin you know is authentic was on the other side, you can identify which side has the fake coin. Again, you’ve used the balance only once to find the fake coin.

This method works because the balance scale gives you more information than a simple weight measurement. It not only tells you whether there is a difference in weight, but also which group of coins is lighter or heavier. By using the known authentic coin as a reference, you can identify the fake coin in just one measurement.

Bard’s Responses

You can determine the fake coin in 3 weighings.

1. Weigh coin 1 against coin 2.
• If they weigh the same, the fake coin is either coin 3 or coin 4.
• If they weigh differently, the fake coin is the heavier coin.
1. Weigh the coin that was not weighed in step 1 against coin 3.
• If they weigh the same, the fake coin is coin 4.
• If they weigh differently, the fake coin is the heavier coin.

Dynamic Pluggable MicroService Framework v3.1 now in Production !!! (raychorn.github.io)