CMIMC 2018 Power Problem 5.2

Assume that c_{i} \neq c_{j} (but the player does not know this in advance).

(a) Show that after 2 \cdot \min \left\{c_{i}, c_{j}\right\}-1 turns, we can determine either of C_{i} or C_{j}.

(b) Show that after \max \left\{2 \cdot \min \left\{c_{i}, c_{j}\right\}-1, c_{i}, c_{j}\right\} turns, we can completely figure out both of C_{i} and C_{j}.