benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / You are the first lucky player to play in a slightly modified episode of Deal or…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

You are the first lucky player to play in a slightly modified episode of Deal or No Deal! Initially, there are sixteen cases marked 1 through 16. The dollar amounts in the cases are the powers of 2 from 21=22^{1}=2 to 216=655362^{16}=65536, in some random order. The game has eight turns. In each turn, you choose a case and claim it, without opening it. Afterwards, a random remaining case is opened and revealed to you, then removed from the game. At the end of the game, all eight of your cases are revealed and you win all of the money inside them. However, the hosts do not realize you have X-ray vision and can see the amount of money inside each case! What is the expected amount of money you will make, given that you play optimally?
Plain-text mathematical notation (without MathML)
You are the first lucky player to play in a slightly modified episode of Deal or No Deal! Initially, there are sixteen cases marked 1 through 16. The dollar amounts in the cases are the powers of 2 from 2¹=2 to 2¹⁶=65536, in some random order. The game has eight turns. In each turn, you choose a case and claim it, without opening it. Afterwards, a random remaining case is opened and revealed to you, then removed from the game. At the end of the game, all eight of your cases are revealed and you win all of the money inside them. However, the hosts do not realize you have X-ray vision and can see the amount of money inside each case! What is the expected amount of money you will make, given that you play optimally?
Original LaTeX notation
You are the first lucky player to play in a slightly modified episode of Deal or No Deal! Initially, there are sixteen cases marked 1 through 16. The dollar amounts in the cases are the powers of 2 from \(2^{1}=2\) to \(2^{16}=65536\), in some random order. The game has eight turns. In each turn, you choose a case and claim it, without opening it. Afterwards, a random remaining case is opened and revealed to you, then removed from the game. At the end of the game, all eight of your cases are revealed and you win all of the money inside them. However, the hosts do not realize you have X-ray vision and can see the amount of money inside each case! What is the expected amount of money you will make, given that you play optimally?

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
75c77391-d0e7-5a1a-9df9-46ed1b816942
task_key
test--75c77391-d0e7-5a1a-9df9-46ed1b816942
task_revision_id
1
config / split
/ test

Official source

initial import