The Martians
Probability
Level
2
The Martians come in a variety of interesting forms. 75% of all Martians are blue. 75% of all Martians have five eyes. 75% of all Martians have six legs. What is the smallest percentage of Martians who are blue, have five eyes, and have six legs? Give your answer as percentage.
The answer is 25.
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1 solution
This is a variation on the pigeon hole principle. Instead of using percentages, imagine that you have 100 Martians. Now 75 are blue, 75 have five eyes, and 75 have six legs. Altogether, there are 225 "qualities" (75 + 75 + 75 = 225). If you distribute these 225 qualities among 100 Martians, at least 25 Martians must have all three qualities.