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In Harmony with averages (Posted on 2010-03-12) Difficulty: 3 of 5
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 Submitted by Ady TZIDON    
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  Subject Author Date
solutionJustin2010-03-12 15:38:05
SolutionA solution that might make sense.Jer2010-03-12 15:07:40
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