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MathNet 2022-part-06 — 196 problems (EN–VI) Question 25

Math Olympiad Vault · MathNet 2022-part-06 — 196 problems (EN–VI)

Question 25

Aerith has 5 coins, all with heads facing up. She wants to flip them so that they all have tails facing up.

a) If she must flip exactly three coins at a time (from heads to tails or vice versa), is this possible?

b) What if she must flip exactly two coins at a time?

For each part, either show a way it can be done or prove that it is impossible.