## Integers

Let a, b, c and d be 4 distinct integers. Find the smallest possible value for $$4(a^2 + b^2 + c^2 + d^2) - (a+b+c+d)^2$$ and prove that your answer is correct.

I got 20 as the smallest answer. Thats when u have a, b, c, and d as 4 consective integers, but i cant prove my answer. Can anyone help? Thanks :)
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 Quote by Pandaren Let a, b, c and d be 4 distinct integers. Find the smallest possible value for $$4(a^2 + b^2 + c^2 + d^2) - (a+b+c+d)^2$$ and prove that your answer is correct. I got 20 as the smallest answer. Thats when u have a, b, c, and d as 4 consective integers, but i cant prove my answer. Can anyone help? Thanks :)
Without having put a lot of thought in at all, can you not just pick numbers 2 apart e.g. 1, 3, 5 and 7 and then 3 apart and prove it that way???

The Bob (2004 )