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Apr 9, 2023< / p > < ul class = tags > < li > < a href = https://ar.falsy.cat/tags/note/ > Note< / a > < / li > < li > < a href = https://ar.falsy.cat/tags/info-tech/ > Info tech< / a > < / li > < li > < a href = https://ar.falsy.cat/tags/logical/ > Logical< / a > < / li > < / ul > < aside class = mainTOC > < details > < summary > Table of Contents< / summary > < nav id = TableOfContents > < ol > < li > < a href = #概要 > 概要< / a > < / li > < li > < a href = #問題の簡潔化 > 問題の簡潔化< / a > < / li > < li > < a href = #解答 > 解答< / a > < / li > < li > < a href = #解説 > 解説< / a > < / li > < li > < a href = #応用 > 応用< / a > < / li > < li > < a href = #参考文献 > 参考文献< / a > < / li > < / ol > < / nav > < / details > < / aside > < a href = #概要 > < h2 id = 概要 > < span class = hanchor arialabel = Anchor > # < / span > 概要< / h2 > < / a > < ul > < li > 「2人の幼女とチェス盤の部屋」という次のような論理問題を解説する< ul > < li > 以下の手順の後， < 64\right)$を求められるようにするには， < ol > < li > 悪魔が8x8チェス盤の各マスに1個ずつ， < / li > < li > 悪魔は幼女Aにチェス盤を見せ， < 64\right)$を伝える< / li > < li > 幼女Aは， < ul > < li > 任意のマスからポーンを1個だけ取り除く< / li > < li > 任意のマスにポーンを1個だけ追加する< / li > < / ul > < / li > < li > 悪魔は幼女Bにチェス盤を見せる< / li > < / ol > < / li > < / ul > < / li > < / ul > < a href = #問題の簡潔化 > < h2 id = 問題の簡潔化 > < span class = hanchor arialabel = Anchor > # < / span > 問題の簡潔化< / h2 > < / a > < ul > < li > $f(g(b,x))=x$とできるような写像$f,g$を求めよ< ul > < li > $B=\left\{0,1\right\}$< / li > < li > $b\in B^{64}$< / li > < li > $x\in B^6$< / li > < li > $f: B^{64} \rightarrow B^6$< / li > < li > $g: \left< B^{64}, B^6\right>\rightarrow B^{64}$< ul > < li > $b$と$g(b,x)$は1ビットだけ異なる< / li > < / ul > < / li > < / ul > < / li > < / ul > < a href = #解答 > < h2 id = 解答 > < span class = hanchor arialabel = Anchor > # < / span > 解答< / h2 > < / a > < ul > < li > $f(b)=f_0\oplus f_1\oplus f_2 \oplus \dots \oplus f_{63} \quad\left(f_i=i b_i\right)$< / li > < li > $b’ =g(b,x) \implies b’ _m \neq b_m\quad\left(m=x\oplus f(b)\right)$< / li > < li > < a href = https://wandbox.org/permlink/XLo1pGURvrU4Y4Jj rel = noopener > チェス盤が16x16の場合のプログラム< / a > < / li > < / ul > < a href = #解説 > < h2 id = 解説 > < span class = hanchor arialabel = Anchor > # < / span > 解説< / h2 > < / a > < ul > < li > $x=f(b)\oplus m$となるような$m\in B^6$は必ず存在する< / li > < li > 盤面の各マスに$m$の値を割り当てることで， < ul > < li > 盤面のマス目の数も，$m$がとりうる値の数も64< / li > < li > $f(g(b,x))=f(b)\oplus m=f(b)\oplus f_m\oplus m(1-b_m)$< / li > < / ul > < / li > < / ul > < a href = #応用 > < h2 id = 応用 > < span class = hanchor arialabel = Anchor > # < / span > 応用< / h2 > < / a > < ul > < li > 長さ$2^{2^N}$の任意のビット列について， ， < / li > < / ul > < a href = #参考文献 > < h2 id = 参考文献 > < span class = hanchor arialabel = Anchor > # < / span > 参考文献< / h2 > < / a > < ul > < li > < a href = https://sist8.com/chess2you rel = noopener > # 超難問論理クイズ「2人の幼女とチェス盤の部屋」が本当に難しすぎた - 明日は未来だ！< / a > < / li > < li > < a href = https://gist.github.com/catupper/5678658 rel = noopener > 幼女問題まとめ - GItHub Gist< / a > < / li > < li > < a href = http://datagenetics.com/blog/december12014/index.html rel = noopener > Impossible Escape? - DataGenetics< / a > < / li > < / ul > < div class = content-list > < h2 > Related Notes< / h2 > < ul class = section-ul > < li class = section-li > < div class = section > < p class = meta > Mar 18, 2023< / p > < div class = desc > < h3 > < a href = https://ar.falsy.cat/note/info-tech/install-archlinux/ class = internal-link data-src = /note/info-tech/install-archlinux/ > ArchLinuxのインストール< / a > < / h3 > < / div > < div class = spacer > < / div > < ul class = tags > < li > < a href = https://ar.falsy.cat/tags/note/ > Note< / a > < / li > < li > < a href = https://ar.falsy.cat/tags/info-tech/ > Info-Tec
