Dan and Dave have just finished sealing up three gigantic crates full of playing cards. One crate is full of blue decks, one crate is full of red decks and one crate is a mix of half red and half blue. Suddenly, they realize that all the crates are mis-labeled. The tricky thing is, every pack of cards is wrapped and sealed in the same brown paper so it’s impossible to know what color the cards are without unwrapping the individual packaging. What is the fewest number of crates and packs of cards that need to be unwrapped for Dan and Dave to know which label belongs on which crate?
Congratulations to everyone who correctly solved this puzzle. We've posted all the answers below. Special shout-out to the first three of you who solved it and won a a hand-turned spinning top: Alain Lacourse, Arvind, and Siddharth Rode.
Solution: It is only necessary to open one deck from the crate labeled "mix of half red and half blue." Because every crate is mis-labeled, whatever color deck is opened from the mixed crate must be that color. Now that this is known, let's say it's the red crate, you will know that the blue labeled crate is actually the mixed crate and that the red labeled crate is actually the blue crate.
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