A game consists of tossing a coin successively. There is an entry fee of $10 and an additional fee of $1 for each toss of the coin. The game is considered to have ended normally when the coin turns heads on two consecutive throws. In this case the player is paid $100. Alternatively, the player can choose to terminate the game prematurely after any of the tosses. Sam has incurred a loss of $50 by playing this game. How many times did he toss the coin?

(1) The game ended normally.

(2) The total number of tails obtained in the game was 138.


OA in the next post.