{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-the-renyi-ulam-game-with-restricted-size","title":"On the Rényi-Ulam Game with Restricted Size Queries","arxiv_id":"2104.01664","date":"2021-04-04","proceeding":null,"authors":["Ádám Fraknói","Dávid Márton","Dániel Simon","Dániel Lenger"],"abstract":"We investigate the following version of the well-known R\\'enyi-Ulam game. Two players - the Questioner and the Responder - play against each other. The Responder thinks of a number from the set $\\{1,\\ldots,n\\}$, and the Questioner has to find this number. To do this, he can ask whether a chosen set of at most $k$ elements contains the thought number. The Responder answers with YES or NO immediately, but during the game, he may lie at most $\\ell$ times. The minimum number of queries needed for the Questioner to surely find the unknown element is denoted by $RU_\\ell^k(n)$. First, we develop a highly effective tool that we call Convexity Lemma. By using this lemma, we give a general lower bound of $RU_\\ell^k(n)$ and an upper bound which differs from the lower one by at most $2\\ell+1$. We also give its exact value when $n$ is sufficiently large compared to $k$. With these, we managed to improve and generalize the results obtained by Meng, Lin, and Yang in a 2013 paper about the case $\\ell=1$.","url_abs":"https://arxiv.org/abs/2104.01664v4","url_pdf":"https://arxiv.org/pdf/2104.01664v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"on-the-renyi-ulam-game-with-restricted-size","repo_url":"https://github.com/fraknoiadam/bounded-renyi-ulam-game","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}