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blog/2023/0301-fukue-island/index.html

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blog/2023/0303-fukue-island/index.html

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blog/2023/0304-fukue-island/index.html

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blog/2023/0319-moving/index.html

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note/chores/one-hand-egg-cracking/index.html

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note/index.html

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note/info-tech/flutter/index.html

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note/info-tech/install-archlinux/index.html

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note/info-tech/library-c-cpp/index.html

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note/info-tech/obsidian/index.html

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note/info-tech/pleroma/index.html

@@ -9,7 +9,7 @@
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note/info-tech/publish-obsidian-by-quartz/index.html

@@ -45,7 +45,7 @@ Quartzの紹介文からの引用
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note/info-tech/qemu/index.html

@@ -33,7 +33,7 @@ M1/M2向けVirtualBoxはまだ開発者プレビューしかなく，まとも
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note/info-tech/tinycthread/index.html

@@ -12,7 +12,7 @@
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note/page/2/index.html

@@ -9,7 +9,7 @@
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note/word-play/japanese-text-all-stars/index.html

@@ -18,7 +18,7 @@
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note/word-play/proof-of-reality-using-lucid-dream/index.html

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tags/blog/index.html

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tags/c-language/index.html

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tags/cat/index.html

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tags/cooking/index.html

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tags/cpp/index.html

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tags/fediverse/index.html

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tags/gourmet/index.html

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tags/index.html

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tags/info-tech/index.html

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tags/library/index.html

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tags/lifehack/index.html

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tags/linux/index.html

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tags/logical/index.html

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tags/logical/index.xml

@@ -1 +1 @@
-<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>logical on</title><link>https://ar.falsy.cat/tags/logical/</link><description>Recent content in logical on</description><generator>Hugo -- gohugo.io</generator><language>en-us</language><atom:link href="https://ar.falsy.cat/tags/logical/index.xml" rel="self" type="application/rss+xml"/><item><title>2人の幼女と悪魔とチェス盤</title><link>https://ar.falsy.cat/note/info-tech/two-lolita-devils-and-chess-board/</link><pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate><guid>https://ar.falsy.cat/note/info-tech/two-lolita-devils-and-chess-board/</guid><description>概要 「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 以下の手順の後，幼女Bが任意の整数$x\left(0\leq x&amp;lt;64\right)$を求められるようにするには，幼女Aはどのような操作を行うべきか 悪魔が8x8チェス盤の各マスに0個以上64個以下のポーンをランダムに配置する 悪魔は幼女Aにチェス盤を見せ，任意の数字$x\left(0\leq x&amp;lt;64\right)$を伝える 幼女Aは，チェス盤に対して次のいずれかの操作のうち可能であるものを1回だけ必ず行う 任意のマスからポーンを1個だけ取り除く 任意のマスにポーンを1個だけ追加する 悪魔は幼女Bにチェス盤を見せる 問題の簡潔化 $f(g(b,x))=x$とできるような写像$f,g$を求めよ $B=\left\{0,1\right\}$ $b\in B^{64}$ $x\in B^6$ $f: B^{64} \rightarrow B^6$ $g: \left&amp;lt;B^{64}, B^6\right&amp;gt;\rightarrow B^{64}$ $b$と$g(b,x)$は1ビットだけ異なる 解答 $f(b)=f_0\oplus f_1\oplus f_2 \oplus \dots \oplus f_{63} \quad\left(f_i=i b_i\right)$ $b&amp;rsquo;=g(b,x) \implies b&amp;rsquo;_m \neq b_m\quad\left(m=x\oplus f(b)\right)$ チェス盤が16x16の場合のプログラム 解説 $x=f(b)\oplus m$となるような$m\in B^6$は必ず存在する 盤面の各マスに$m$の値を割り当てることで，1マスの操作だけで$m$を表現できる 盤面のマス目の数も，$m$がとりうる値の数も64 $f(g(b,x))=f(b)\oplus m=f(b)\oplus f_m\oplus i(1-b_i)$ 応用 長さ$2^{2^N}$の任意のビット列について，任意の1ビットだけを反転させることで，長さ$2^N$のビット列を表現できる 参考文献 # 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！ 幼女問題まとめ - GItHub Gist Impossible Escape?</description></item></channel></rss>
+<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>logical on</title><link>https://ar.falsy.cat/tags/logical/</link><description>Recent content in logical on</description><generator>Hugo -- gohugo.io</generator><language>en-us</language><atom:link href="https://ar.falsy.cat/tags/logical/index.xml" rel="self" type="application/rss+xml"/><item><title>2人の幼女と悪魔とチェス盤</title><link>https://ar.falsy.cat/note/info-tech/two-lolita-devils-and-chess-board/</link><pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate><guid>https://ar.falsy.cat/note/info-tech/two-lolita-devils-and-chess-board/</guid><description>概要 「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 以下の手順の後，幼女Bが任意の整数$x\left(0\leq x&amp;lt;64\right)$を求められるようにするには，幼女Aはどのような操作を行うべきか 悪魔が8x8チェス盤の各マスに1個ずつ，合計0個以上64個以下のポーンをランダムに配置する 悪魔は幼女Aにチェス盤を見せ，任意の数字$x\left(0\leq x&amp;lt;64\right)$を伝える 幼女Aは，チェス盤に対して次のいずれかの操作のうち可能であるものを1回だけ必ず行う 任意のマスからポーンを1個だけ取り除く 任意のマスにポーンを1個だけ追加する 悪魔は幼女Bにチェス盤を見せる 問題の簡潔化 $f(g(b,x))=x$とできるような写像$f,g$を求めよ $B=\left\{0,1\right\}$ $b\in B^{64}$ $x\in B^6$ $f: B^{64} \rightarrow B^6$ $g: \left&amp;lt;B^{64}, B^6\right&amp;gt;\rightarrow B^{64}$ $b$と$g(b,x)$は1ビットだけ異なる 解答 $f(b)=f_0\oplus f_1\oplus f_2 \oplus \dots \oplus f_{63} \quad\left(f_i=i b_i\right)$ $b&amp;rsquo;=g(b,x) \implies b&amp;rsquo;_m \neq b_m\quad\left(m=x\oplus f(b)\right)$ チェス盤が16x16の場合のプログラム 解説 $x=f(b)\oplus m$となるような$m\in B^6$は必ず存在する 盤面の各マスに$m$の値を割り当てることで，1マスの操作だけで$m$を表現できる 盤面のマス目の数も，$m$がとりうる値の数も64 $f(g(b,x))=f(b)\oplus m=f(b)\oplus f_m\oplus m(1-b_m)$ 応用 長さ$2^{2^N}$の任意のビット列について，任意の1ビットだけを反転させることで，長さ$2^N$のビット列を表現できる 参考文献 # 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！ 幼女問題まとめ - GItHub Gist Impossible Escape?</description></item></channel></rss>

tags/mountain/index.html

@@ -9,7 +9,7 @@
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tags/note/index.html

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tags/note/page/2/index.html

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tags/photo/index.html

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tags/sns/index.html

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tags/software/index.html

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tags/tool/index.html

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tags/travel/index.html

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tags/virtualization/index.html

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tags/web/index.html

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tags/word-play/index.html

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