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Pick up a number, say 12. Write down a list of all its divisors, including the number itself.

In our case: 1,2,3,4,6,12. Now evaluate AA and HA- the arithmetic and the harmonic averages.

AA=(1+2+3+4+6+12)/6=28/6
HA=6/(1/1+1/2+1/3+1/4+1/6+1/12)=6*12/28

Now evaluate the product AA*HA: (28/6)*(6*12/28)

Surprise, surprise! - the answer is 12, a number picked by us.

Please explain why it works with any number.

(No Solution Yet, 2 Comments) Submitted on 2010-03-12 by Ady TZIDON   
Difficulty: 3 of 5 Bonus: The three daughters (in Logic) Rating: 3.29
A man in my neighbourhood has three daughters. One day when I asked their ages he said:

"The product of their ages is 36".

When I still couldn't find their ages he said:

"Ok. I'll give you another clue: the sum of their ages is same as the number of my house".

I knew the number but still couldn't calculate their ages. So the man gave me a last hint, he said:

"My eldest daughter lives upstairs".

Finally I was able to find their ages. Can you?

(Solution Posted, 15 Comments) Submitted on 2002-10-31 by maverick   
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