Question

2,6,10,14,18,22,26,30,34,38,42,46,50,54,58 * The sum of any 3 of these numbers should be 60

Answer 1

Answer:

It's impossible. All the numbers in the list are just 2∗2∗(odd number) from 1 to 29.Now, add up any three of them. Let's say the 3 odd numbers you choose are a,b,ca,b,cSo, 2a + 2b + 2c = 602(a + b + c) = 2(30)But, since a, b and c are all odd, their sum must always be an odd number. Why? Because:odd + odd + odd = (odd + odd) + odd= even + odd = oddSince 3 odd numbers always add up to another odd number, their sum cannot be 30. Thus, it is not possible to add three of those numbers to give you 60, or any number divisible by 4.

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