<s>[INST] If sum of $N$ natural numbers is less than $N+2$ then each of these numbers is less than $3$. Prove by contradiction. 
If sum of $N$ natural numbers is less than $N+2$ then each of these numbers is less than $3$.
Attempt:
Assume if the sum of $N$ natural numbers is less than $N+2$ then each of these numbers is greater than $3$.
Let $x$ be the sum of $N$ natural numbers
$x < N + 2 $
 [/INST] Try this:
Assume the sum of $N$ natural numbers is less than $N+2 \implies$ at least one of these numbers is not less than $3$.
Call that number $Y$. But then $Y+2 \ge 3+2=5.$ But $5 > N+2 \implies$ Contradiction!
$\therefore$ the sum of $N$ natural numbers is less than $N+2 \implies$ each of these numbers is less than $3$.
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