2.1 KiB
id | challengeType | title | forumTopicId |
---|---|---|---|
5900f52a1000cf542c51003b | 5 | Problem 444: The Roundtable Lottery | 302116 |
Description
An arbitrary person is chosen to be the first player. Going around the table, each player has only one of two options:
- The player can scratch his ticket and reveal its worth to everyone at the table.
- The player can trade his unscratched ticket for a previous player's scratched ticket, and then leave the game with that ticket. The previous player then scratches his newly-acquired ticket and reveals its worth to everyone at the table.
The game ends once all tickets have been scratched. All players still remaining at the table must leave with their currently-held tickets.
Assume that each player uses the optimal strategy for maximizing the expected value of his ticket winnings.
Let E(p) represent the expected number of players left at the table when the game ends in a game consisting of p players (e.g. E(111) = 5.2912 when rounded to 5 significant digits).
Let S1(N) = E(p) Let Sk(N) = Sk-1(p) for k > 1
Find S20(1014) and write the answer in scientific notation rounded to 10 significant digits. Use a lowercase e to separate mantissa and exponent (e.g. S3(100) = 5.983679014e5).
Instructions
Tests
tests:
- text: <code>euler444()</code> should return 1.200856722e+263.
testString: assert.strictEqual(euler444(), 1.200856722e+263);
Challenge Seed
function euler444() {
return true;
}
euler444();
Solution
// solution required