# Maths problem

Thursday 9th July 2020

\(a\), \(b\), \(c\), \(d\), \(e\) and \(f\) are positive real numbers with the property that \(a+b+c+d+e+f=20\).

What is the smallest possible value of \(\sqrt{a^2+1^2}+\sqrt{b^2+2^2}+\sqrt{c^2+3^2}+\sqrt{d^2+4^2}+\sqrt{e^2+5^2}+\sqrt{f^2+6^2}\;\)?

Does the diagram below help you?

By **Chris Luke**