{"paper":{"title":"Finding a non-minority ball with majority answers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bal\\'azs Keszegh, Bal\\'azs Patk\\'os, D\\'aniel Gerbner, D\\\"om\\\"ot\\\"or P\\'alv\\\"olgyi, G\\'abor Wiener, M\\'at\\'e Vizer","submitted_at":"2015-09-28T11:22:54Z","abstract_excerpt":"Suppose we are given a set of $n$ balls $\\{b_1,\\ldots,b_n\\}$ each colored either red or blue in some way unknown to us. To find out some information about the colors, we can query any triple of balls $\\{b_{i_1},b_{i_2},b_{i_3}\\}$. As an answer to such a query we obtain (the index of) a {\\em majority ball}, that is, a ball whose color is the same as the color of another ball from the triple. Our goal is to find a {\\em non-minority ball}, that is, a ball whose color occurs at least $\\frac n2$ times among the $n$ balls. We show that the minimum number of queries needed to solve this problem is $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08276","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"}