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.
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?
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