100 Day Summer Challenge

100 problems in 100 days. #100problems

Day 4

4 of 100: Pure Gold

Probability

All of these coins have one gold side and one silver side. You are only allowed to flip over pairs of adjacent coins. For which of these arrangements of 9 coins is it possible to make the entire row gold?

There's a lot going on here! Can you generalize your answer into a rule for when it's possible and when it's impossible to transform an arrangement to pure gold? When it's possible, how can you do it in the fewest number of flips? What if you could flip three adjacent coins instead of two?

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