4
$\begingroup$

We know that $0\leq a \leq b \leq c\leq d\leq e\,\,\text{ and}\,\, a + b + c + d + e = 100$. What would be the least possible value of $\,\,a + c + e\,\,$ ?

I apologize for poor syntax.

1 Answers 1

8

$2(a+c+e) =a+a+c+c+e+e \geq a+b+c+d+e =100$

With equality if and only if $a=0$, $b=c$ and $d=e$.

  • 1
    Equivalently, $a+c+e \ge 0 + b + d$ so $a+c+e \ge \frac{100}{2} = 50$ with equality iff...2012-06-14