benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / A deck of 100 cards is labeled 1,2,…,100 from top to bottom. The top two cards are drawn; one of them is discarded at random, and the other is inserted back at the bottom of the de…

Problem

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

problem

A deck of 100 cards is labeled 1,2,…,1001,2, \ldots, 100 from top to bottom. The top two cards are drawn; one of them is discarded at random, and the other is inserted back at the bottom of the deck. This process is repeated until only one card remains in the deck. Compute the expected value of the label of the remaining card.
Plain-text mathematical notation (without MathML)
A deck of 100 cards is labeled 1,2,…,100 from top to bottom. The top two cards are drawn; one of them is discarded at random, and the other is inserted back at the bottom of the deck. This process is repeated until only one card remains in the deck. Compute the expected value of the label of the remaining card.
Original LaTeX notation
A deck of 100 cards is labeled $1,2, \ldots, 100$ from top to bottom. The top two cards are drawn; one of them is discarded at random, and the other is inserted back at the bottom of the deck. This process is repeated until only one card remains in the deck. Compute the expected value of the label of the remaining card.

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
b9f52e16-4a91-5d9d-a29e-e859cff49e89
task_key
test--b9f52e16-4a91-5d9d-a29e-e859cff49e89
task_revision_id
1
config / split
/ test

Official source

initial import