Every week, the Heartbreak Hotel raffles off a night in its King Suite. The directors select the winning numbers by rolling three standard dice and multiplying their numbers together.
Since only one prize is awarded and the highest winning number is 216 (6 x 6 x 6), the hotel sells 216 tickets, each of which is stamped with a different number from 1 to 216. To enter the raffle,
you buy one or more tickets at $1 each, selecting their numbers from those that have not been purchased.
Assuming that you're the first player and that all the numbers are available:
1. How many tickets would you have to buy to be certain of winning?
Extra credit:
2. How many tickets would you have to buy to have at least a 51% chance of winning?