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<p>An <i>n</i>-element set contains an unknown number of “excellent” elements and we want to find one. The members of a family <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({{\mathcal {F}}}\subset 2^{[n]} \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">F</mi> <mo>⊂</mo> <msup> <mn>2</mn> <mrow> <mo stretchy="false">[</mo> <mi>n</mi> <mo stretchy="false">]</mo> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> of subsets can be asked if they contain at least one excellent element or not. At most one of the answers can be wrong. We find the smallest family that finds one excellent element or claims that there is none.</p>

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Finding One Excellent Element in Case of One Lie

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月18日

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  • Aanchal Gupta,
  • Gyula O. H. Katona

摘要

An n-element set contains an unknown number of “excellent” elements and we want to find one. The members of a family \({{\mathcal {F}}}\subset 2^{[n]} \) F ⊂ 2 [ n ] of subsets can be asked if they contain at least one excellent element or not. At most one of the answers can be wrong. We find the smallest family that finds one excellent element or claims that there is none.