75% of men from a certain group are tall, 75% have brown hair, and 75% have brown eyes. What is the minimum percentage that are tall, have brown hair,

*and*have brown eyes? Click below to see the answer.

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## Saturday, August 12, 2017

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Minimum Percentage

75% of men from a certain group are tall, 75% have brown hair, and 75% have brown eyes. What is the minimum percentage that are tall, have brown hair,*and* have brown eyes? Click below to see the answer.

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"The time has come," the Walrus said, "To talk of many things..."

75% of men from a certain group are tall, 75% have brown hair, and 75% have brown eyes. What is the minimum percentage that are tall, have brown hair,

Instead of thinking in percentages to solve this problem, it's helpful to think back to the Pigeonhole Principle. Think of a group of 100 men, then 75 are tall, 75 have brown hair, and 75 have brown eyes. That's 225 individual attributes to assign to 100 men, so at least 25 of them (or **25%**) must have each of the three attributes.

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