Problem of the Week

Problem 7 hint

A sign error in the hint for part (i) has been corrected.

We haven’t yet received any solutions to Problem 7

(i) $(\sqrt{x_1}-\sqrt{x_2})^2 \ge 0$
(ii) A $kl$ -list can be broken up into $k$ separate $l$ -lists. The mean of the means of the $l$ -lists is the mean of the $kl$ -list. (In case it isn’t clear, a $kl$ -list is a list containing $k \times l$ numbers.)
(iii) Appending the mean to a $k$ -list results in a $k+1$ -list with the same mean.
(iv) Proof by induction.