Gold, Silver, and Bronze Coins
Here’s a neat coin puzzle I received by email from my reader s_hskz2 (at twitter.com).
Puzzle. You have 9 coins: 3 gold coins, 3 silver coins, and 3 bronze coins. Within each metal, the coins are indistinguishable. Exactly one gold, one silver, and one bronze coin are counterfeit; the other six are genuine. You are provided with a magic bag that functions as follows: when you place a subset of coins into the bag and cast a spell, the bag glows if and only if the subset contains all three counterfeit coins. Can you identify all three counterfeit coins using at most 5 tests?
I tried to find an easy solution and didn’t. Then I decided to use information theory to guide me to an answer. Unsurprisingly, it worked. The solution wasn’t trivial, but it was a lovely practice in using information theory for such puzzles.
Later, s_hskz2 sent me a more difficult version: There are 10 coins of each kind, and you are allowed to test 10 times, but I was too lazy to try.
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