Puzzle 71 - solution

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The question was

The following characteristics apply to a group of people in a room:

Fourteen are blonds, eight are blue-eyed, and two are neither blond nor blue-eyed. If five of the people are blue-eyed blonds, how many people are in the room?

 

Solution : 

 Let us try to understand this with a diagram


In this diagram

  • a = blue eyed people who are not blond     b - blond people who are not blue eyed
  • c - both blond and blue eyed      d - neither blond nor blue eyed (which is 2)

We know that c = 5. And a+c (blue eyed people)= 8. Which means a  = 8-5 = 3

We also know that b+c = number of blonds  = 14. So b = 14 - 5 = 9

Now total number of people in the party  = a+ b+c+d = 3+9+5+2 = 19

So c is the correct answer.


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