Question 43
a) There are three numbers $a$, $b$, $c$ such that $a \le b \le c$. Let $p$, $q$, $r$ be the pairwise sums $a+b$, $b+c$, $c+a$ in the order such that $p \le q \le r$. Given that $r-q = q-p$, is it certainly true that $c-b = b-a$?
b) There are four numbers $e$, $f$, $g$, $h$ such that $e \le f \le g \le h$. Let $u$, $v$, $w$, $x$, $y$, $z$ be the pairwise sums of those numbers, in the order $u \le v \le w \le x \le y \le z$. Given that $z-y = y-x = x-w = w-v = v-u$, is it certainly true that $h-g = g-f = f-e$?
b) There are four numbers $e$, $f$, $g$, $h$ such that $e \le f \le g \le h$. Let $u$, $v$, $w$, $x$, $y$, $z$ be the pairwise sums of those numbers, in the order $u \le v \le w \le x \le y \le z$. Given that $z-y = y-x = x-w = w-v = v-u$, is it certainly true that $h-g = g-f = f-e$?