Question 18
Five friends, Arnaldo, Bernaldo, Cernaldo, Dernaldo, and Ernaldo, competed in five races. In each race first place earned $5$ points, second $4$, and so on down to last place with $1$. Final scores were the sums over five races. Arnaldo finished first overall with $19$ points, followed by Bernaldo with $16$. Cernaldo, Dernaldo, and Ernaldo were third, fourth, and fifth overall. There were no ties in any race or in the final standings. Curiously, neither Arnaldo nor Bernaldo won even one race.
(a) Show that in every race Arnaldo and Bernaldo occupied second and third places in some order.
(b) How many points did Cernaldo score?
(c) How many races did each runner win?
(a) Show that in every race Arnaldo and Bernaldo occupied second and third places in some order.
(b) How many points did Cernaldo score?
(c) How many races did each runner win?