Question 46
Ara and Bea play a game where they take turns putting numbers from $1$ to $5$ into the cells of the $X$-shaped diagram on the right. Each number must be played exactly once, and a cell cannot have more than one number placed in it. Ara's goal is for the two diagonals of the $X$ diagram to have the same sum when the game is over; Bea's goal is for these two sums to be unequal.
a) Show that Ara can always win if he goes first.
b) Show that Bea can always win if she goes first.
a) Show that Ara can always win if he goes first.
b) Show that Bea can always win if she goes first.