July 1, 2010

Puzzle Of The Day

QUESTION:- Six women have gathered at a friend’s house for afternoon tea. While they are chatting, the doorbell rings. There is a census officer at the door who wants to note down their ages. The women are scandalized at the thought of revealing their true ages. Then the census officer offers a compromise. He says that his requirement will be fulfilled if he can get the average age of the women.
Can you think of a way by which the census officer can know the average age of the women without any of them knowing anyone else’s age?
Condition 1 – The women need to know the average age that the census officer puts in his report.
Condition 2 – The women are really paranoid - they do not want anyone else to know the numerical value of their ages, even if you cannot match the age with the actual person.
Note 1: If we remove the first condition, then the problem becomes somewhat simpler. If we remove the second condition then there are many simple solutions. No prizes for getting the solution after removing either of the conditions – but please do share these solutions in the comments section.
Note 2: There are many solutions that can satisfy all the conditions stated in the puzzle.
Let us get those Grey cells working!

Solution
Solution 1: They divide the women into two groups of 3 each. Each woman in the first group adds 1 (or some other common number) to her age and each woman in the second group subtracts 1 from her age. Each of them secretly writes down this number (after adding or subtracting 1 from the age) on a piece of paper, folds it and then drops it in a bowl. All the papers are opened and average of the numbers on them taken. This average is the average age of the women.

Solution 2: The census officer whispers a random number in the ear of one of the women. She adds her age to that number and whispers the sum in the ear of the second woman. The second woman adds her age to this number and whispers the sum in the ear of the third woman. And so on. The sixth woman tells the final sum to the census officer. He subtracts the original random number from this sum and divides the difference by 6 to obtain the average age.
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