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copied!<p>So let's call the persons B C F M S.</p> <p>Basically everyone can live anywhere, so we have this starting situation:</p> <pre><code>[BCFMS] [BCFMS] [BCFMS] [BCFMS] [BCFMS] </code></pre> <p>Now you do say</p> <blockquote> <p>Baker does not live on the top floor.</p> </blockquote> <p>So We'll have</p> <pre><code>[BCFMS] [BCFMS] [BCFMS] [BCFMS] [CFMS] </code></pre> <blockquote> <p>Cooper does not live on the bottom floor.</p> </blockquote> <p>So we end up with:</p> <pre><code>[BFMS] [BCFMS] [BCFMS] [BCFMS] [CFMS] </code></pre> <blockquote> <p>Fletcher does not live on either the top or the bottom floor.</p> </blockquote> <p>Ookay:</p> <pre><code>[BMS] [BCFMS] [BCFMS] [BCFMS] [CMS] </code></pre> <blockquote> <p>Miller lives on a higher floor than does Cooper.</p> </blockquote> <p>Ok, so M cannot be on a lower position than C:</p> <pre><code>[BS] [BCFS] [BCFMS] [BCFMS] [CMS] </code></pre> <p>And also, C cannot be on the last floor, because M must be above him:</p> <pre><code>[BS] [BCFS] [BCFMS] [BCFMS] [MS] </code></pre> <blockquote> <p>(A): Smith does not live on a floor adjacent to Fletcher’s.</p> <p>(B): Fletcher does not live on a floor adjacent to Cooper’s. </p> </blockquote> <p>So there's no S-F, F-S, F-C or C-F on adjacent "boxes" (floors).</p> <p>And we also know that</p> <blockquote> <p>(C): live on different floors of an apartment house</p> </blockquote> <p>Conforming to (C), we have two possible situations, the first floor being B's or S's</p> <p>Let's take the second case (because we know (A) about him)</p> <pre><code>[S] [BCFS] [BCFMS] [BCFMS] [MS] </code></pre> <p>According to (A):</p> <pre><code>[S] [BC] [BCF] [BCF] [M] </code></pre> <p>So we also know that M lives above C (the previous step is true already, as we know M for sure being on the last floor by now):</p> <pre><code>[S] [BC] [BCF] [BCF] [M] </code></pre> <p>According to (B), neither F nor C can be on the 3rd floor, and under the influence of (C), we ultimately get the only one possible permutation because of further reductions (only one person per floor):</p> <pre><code>[S] [C] [B] [F] [M] </code></pre> <p>So here is the solution:</p> <p><strong>Smith, Cooper, Baker, Fletcher, Miller</strong></p>

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