Question 23

A teacher asks 10 of her students to guess her age. They guessed it as 34, 38, 40, 42, 46, 48, 51, 54, 57 and 59. Teacher said "At least half of you guessed it too low and two of you are off by one. Also my age is a prime number". The teacher's age is

Correct Answer: 47

Solution

The only candidate ages with two guesses exactly one away are the midpoints of consecutive guesses differing by 2, namely 39, 41, 47 and 58, and among these only 41 and 47 are prime. Since 47 has exactly 5 guesses below it (satisfying "at least half too low") while 41 only has 3, the teacher's age is 47.

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A teacher asks 10 of her students to guess her age. They guessed it as 34, 38, 40, 42, 46, 48, 51, 54, 57 and 59. Teacher said "At least half of you guessed it too low and two of you are off by one. Also my age is a prime number". The teacher's age is

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