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        <title>Puzzle Library</title>
        <link>https://puzzle.dezhonger.com/</link>
        <description>Curious problems, puzzles, and notes about beautiful ideas.</description>
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        <item>
            <title><![CDATA[Path 1 or 2 in directed graph]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1999-10-path-one-or-two-in-directed-graph</link>
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            <pubDate>Sat, 05 Sep 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[A directed graph has either a direct edge or one two-step path between every ordered pair. How many vertices does it have?]]></description>
        </item>
        <item>
            <title><![CDATA[Cutting a cube into a box]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1999-11-cutting-a-cube-into-a-box</link>
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            <pubDate>Sat, 05 Sep 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Cut a 12 cm cube into four pieces that reassemble as an 8 by 8 by 27 cm box.]]></description>
        </item>
        <item>
            <title><![CDATA[Zero-less multiple of 2^1999]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1999-12-zero-less-multiple-of-two-power-1999</link>
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            <pubDate>Sat, 05 Sep 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Does 2^1999 have a positive decimal multiple containing no digit zero?]]></description>
        </item>
        <item>
            <title><![CDATA[Catching baseball]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-2000-01-catching-baseball</link>
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            <pubDate>Sat, 05 Sep 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Using only a fly ball’s changing elevation angle, decide whether an outfielder should move forward or backward.]]></description>
        </item>
        <item>
            <title><![CDATA[Wally's Rock Permuting (WRP)]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1999-04-wallys-rock-permuting</link>
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            <pubDate>Mon, 31 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[A paid service can swap any collection of disjoint rock pairs in one call. What is the worst-case cost to sort N rocks?]]></description>
        </item>
        <item>
            <title><![CDATA[Integer side rectangles partition]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1999-05-integer-side-rectangles-partition</link>
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            <pubDate>Mon, 31 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[If every aligned small rectangle has an integer side, must the large rectangle have an integer side too?]]></description>
        </item>
        <item>
            <title><![CDATA[1 plus 1/7 of the medals]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1999-06-one-plus-one-seventh-of-the-medals</link>
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            <pubDate>Mon, 31 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[A competition distributes a day number plus one seventh of the remaining medals each day. How long does it last?]]></description>
        </item>
        <item>
            <title><![CDATA[Labeling bowling pins]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1999-07-labeling-bowling-pins</link>
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            <pubDate>Mon, 31 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Label ten triangularly arranged pins with 0 through 9 under a modular adjacent-sum rule.]]></description>
        </item>
        <item>
            <title><![CDATA[Seating people on N+M tables]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1999-08-seating-people-on-n-plus-m-tables</link>
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            <pubDate>Mon, 31 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[How many meals let every pair among M+N people share a table at least once?]]></description>
        </item>
        <item>
            <title><![CDATA[Recognizing dishes]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1999-09-recognizing-dishes</link>
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            <pubDate>Mon, 31 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Can five diners identify all nine unknown dishes after three meals, and why does ten make this impossible?]]></description>
        </item>
        <item>
            <title><![CDATA[Even Fibonacci Numbers]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/even-fibonacci-numbers</link>
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            <pubDate>Wed, 26 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Project Euler Problem 2, formalized as a bounded sequence sum and solved by advancing directly between even terms.]]></description>
        </item>
        <item>
            <title><![CDATA[Cutting frosted cake]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1998-11-cutting-frosted-cake</link>
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            <pubDate>Tue, 25 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Divide a square or rectangular frosted cake among N guests with cake and frosting equal for everyone.]]></description>
        </item>
        <item>
            <title><![CDATA[Removing snow]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1998-12-removing-snow</link>
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            <pubDate>Tue, 25 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Two distance observations of a constant-rate snowplow determine when the steady snowfall began.]]></description>
        </item>
        <item>
            <title><![CDATA[Water glass center of mass]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1999-01-water-glass-center-of-mass</link>
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            <pubDate>Tue, 25 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[The water depth at the lowest center of mass reveals the mass of a cylindrical tumbler.]]></description>
        </item>
        <item>
            <title><![CDATA[A leashed sheep eats grass]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1999-02-a-leashed-sheep-eats-grass</link>
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            <pubDate>Tue, 25 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Find the leash length that lets a sheep tied at a circular field’s edge graze exactly half its grass.]]></description>
        </item>
        <item>
            <title><![CDATA[Cliques of people in a ballroom]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1999-03-cliques-of-people-in-a-ballroom</link>
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            <pubDate>Tue, 25 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[How does a minimum acquaintance count force, or fail to force, a four-person clique?]]></description>
        </item>
        <item>
            <title><![CDATA[A belt around the earth]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1998-05-belt-around-the-earth</link>
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            <pubDate>Thu, 20 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Six extra metres, one lifted point, and a height that defies first intuition.]]></description>
        </item>
        <item>
            <title><![CDATA[Shaking hands in a party]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1998-06-shaking-hands-in-a-party</link>
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            <pubDate>Thu, 20 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Seven distinct answers about handshakes reveal a hidden structure among four couples.]]></description>
        </item>
        <item>
            <title><![CDATA[Tennis balls in a bucket]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1998-07-tennis-balls-in-a-bucket</link>
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            <pubDate>Thu, 20 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Arrange distinct positive counts in rows of three while making their common sum as small as possible.]]></description>
        </item>
        <item>
            <title><![CDATA[Equilateral triangle]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1998-08-equilateral-triangle</link>
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            <pubDate>Thu, 20 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[A small equilateral triangle with cyclically equal offsets forces the outer triangle to be equilateral too.]]></description>
        </item>
        <item>
            <title><![CDATA[Magic Star of David]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1998-09-magic-star-of-david</link>
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            <pubDate>Thu, 20 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Place 1 through 12 on a six-pointed star so every one of its six lines has the same sum.]]></description>
        </item>
        <item>
            <title><![CDATA[Sorting pancakes]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/ponder-this-1998-10-sorting-pancakes</link>
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            <pubDate>Thu, 20 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[How many prefix reversals can the hardest permutation of differently sized pancakes require?]]></description>
        </item>
        <item>
            <title><![CDATA[Drawing the Right Diagram]]></title>
            <link>https://puzzle.dezhonger.com/notes/drawing-the-right-diagram</link>
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            <pubDate>Mon, 17 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Why one auxiliary line can be more valuable than a page of algebra.]]></description>
        </item>
        <item>
            <title><![CDATA[Invariants as Conservation Laws]]></title>
            <link>https://puzzle.dezhonger.com/notes/invariants-as-conservation-laws</link>
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            <pubDate>Mon, 17 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[A practical way to search for the quantity a legal move cannot change.]]></description>
        </item>
        <item>
            <title><![CDATA[When Symmetry Counts Too Much]]></title>
            <link>https://puzzle.dezhonger.com/notes/when-symmetry-counts-too-much</link>
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            <pubDate>Mon, 17 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Orbit thinking, Burnside’s lemma, and the warning signs of accidental overcounting.]]></description>
        </item>
        <item>
            <title><![CDATA[Conway's Soldiers]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/conways-soldiers</link>
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            <pubDate>Mon, 17 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[How far can an army of pegs advance when every move must be a jump?]]></description>
        </item>
        <item>
            <title><![CDATA[Largest Prime Factor]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/largest-prime-factor</link>
            <guid isPermaLink="false">https://puzzle.dezhonger.com/puzzles/largest-prime-factor</guid>
            <pubDate>Mon, 17 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Project Euler Problem 3, formalized as a maximization over prime divisors and solved by repeated trial division.]]></description>
        </item>
        <item>
            <title><![CDATA[The Monty Hall Paradox]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/monty-hall-paradox</link>
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            <pubDate>Mon, 17 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[One prize, three doors, and an informed host: should you switch?]]></description>
        </item>
        <item>
            <title><![CDATA[Morley's Miracle]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/morleys-miracle</link>
            <guid isPermaLink="false">https://puzzle.dezhonger.com/puzzles/morleys-miracle</guid>
            <pubDate>Mon, 17 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Adjacent angle trisectors of an arbitrary triangle form an equilateral triangle.]]></description>
        </item>
        <item>
            <title><![CDATA[Multiples of 3 or 5]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/multiples-of-3-or-5</link>
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            <pubDate>Mon, 17 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Project Euler Problem 1, stated precisely and solved with arithmetic progressions and inclusion–exclusion.]]></description>
        </item>
        <item>
            <title><![CDATA[The 100 Prisoners Problem]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/the-100-prisoners-problem</link>
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            <pubDate>Mon, 17 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[A cycle-following strategy turns an almost impossible search into a surprisingly hopeful one.]]></description>
        </item>
        <item>
            <title><![CDATA[The Mutilated Chessboard]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/the-mutilated-chessboard</link>
            <guid isPermaLink="false">https://puzzle.dezhonger.com/puzzles/the-mutilated-chessboard</guid>
            <pubDate>Mon, 17 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Two missing corners, thirty-one dominoes, and one coloring that settles everything.]]></description>
        </item>
        <item>
            <title><![CDATA[The Nine-Point Circle]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/the-nine-point-circle</link>
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            <pubDate>Mon, 17 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Nine distinguished points of every triangle quietly share a single circle.]]></description>
        </item>
        <item>
            <title><![CDATA[The Two Envelope Problem]]></title>
            <link>https://puzzle.dezhonger.com/puzzles/the-two-envelope-problem</link>
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            <pubDate>Mon, 17 Aug 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[A seductive expected-value argument seems to say that switching is always better.]]></description>
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