How can be get 60 by adding starting from 2 and adding 4 again and again
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How can we get 60 by adding only three numbers out of these: 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, & 58?
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Given numbers are of the form (2k-1)2 for k from 1 to 30.
If we take 3 numbers then they are (2a-1)2, (2b-1)2 and (2b-1)2 for some natural numbers a, b and c between 1 and 30 (both inclusive.
The numbers add up to
(2a-1)2+(2b-1)2+(2c-1)2
=(2a-1+2b-1+2c-1)2
=(2(a+b+c)-3)2
So, we get equation
(2(a+b+c)-3)2=60
=>2(a+b+c)-3=30
=>2(a+b+c)-3=30
=>2(a+b+c)=33
33 being odd, it cannot be double of sum of natural numbers
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