{"paper":{"title":"Playing Mastermind with Many Colors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Benjamin Doerr, Carola Doerr, Henning Thomas, Reto Sp\\\"ohel","submitted_at":"2012-07-03T18:32:08Z","abstract_excerpt":"We analyze the general version of the classic guessing game Mastermind with $n$ positions and $k$ colors. Since the case $k \\le n^{1-\\varepsilon}$, $\\varepsilon>0$ a constant, is well understood, we concentrate on larger numbers of colors. For the most prominent case $k = n$, our results imply that Codebreaker can find the secret code with $O(n \\log \\log n)$ guesses. This bound is valid also when only black answer-pegs are used. It improves the $O(n \\log n)$ bound first proven by Chv\\'atal (Combinatorica 3 (1983), 325--329). We also show that if both black and white answer-pegs are used, then "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0773","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}