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 filifa
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filifa
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<!doctype html>
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<html lang="en-US">
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<head>
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<meta charset="utf-8" />
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<meta name="viewport" content="width=device-width,initial-scale=1" />
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<link rel="stylesheet" href="/styles/default.css" />
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<link rel="icon" href="/images/favicon.ico" />
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<title>I'm bored.</title>
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</head>
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<body>
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<header>
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<a id="homelink" href="/">dairydemon.net</a>
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</header>
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<main>
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<article>
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<h1>I'm bored.</h1>
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<h2>Word games</h2>
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<ul>
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<li><strong><a href="https://www.theatlantic.com/games/bracket-city/">Bracket City</a>: Daily game. Easier to play than explain.</strong></li>
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<li><a href="https://www.sporcle.com/acrostic/">Sporcle Daily Acrostic</a>: Daily game.</li>
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<li><a href="https://raddle.quest/">Raddle</a>: Daily game. The tutorial explains it better than I can.</li>
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</ul>
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<h2>Trivia games</h2>
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<ul>
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<li><a href="https://www.sporcle.com/">Sporcle</a>: Just in case you haven't heard of it.</li>
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<li><strong><a href="https://thrice.geekswhodrink.com/">Thrice</a>: Fun daily trivia game.</strong></li>
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<li><a href="https://www.qbreader.org/">QB Reader</a>: Play quizbowl!</li>
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<li><strong><a href="https://catfishing.net/">Catfishing</a>: Daily game. Guess Wikipedia articles from their category lists.</strong></li>
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</ul>
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<h2>Logic games</h2>
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<ul>
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<li><a href="https://www.chiark.greenend.org.uk/~sgtatham/puzzles/">Simon Tatham's Portable Puzzle Collection</a>: A bunch of puzzle games. Some of my favorites are Map, Mines, Net, Rectangles, Singles, and Untangle.</li>
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<li><a href="https://www.puzzle-star-battle.com/">Puzzle Team</a>: Some overlap with Simon Tatham's, but also has some fun ones like Star Battle.</li>
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<li><strong><a href="https://puzzmallow.com/buzzled">Buzzled</a>: Fun daily logic puzzle game.</strong></li>
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<li><a href="https://puzzarium.com/every-5x6-nonogram">Every 5x6 Nonogram</a>: I think this is technically an MMO?</li>
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</ul>
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<h2>More games</h2>
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<ul>
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<li><a href="https://redactle.net/">Redactle</a>: Daily game. Guess a Wikipedia article word-by-word.</li>
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<li><a href="https://www.sports-reference.com/immaculate-grid/">Immaculate Grid</a>: Daily game. I only occasionally play the baseball flavor of this one, and I'm pretty bad at it.</li>
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<li><strong><a href="https://enclose.horse/">Enclose.horse</a>: Daily game where you enclose a horse. (The tutorial explains it better than I can.) Very cute design, which masks how challenging the puzzles can be.</strong></li>
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<li><a href="https://nandgame.com/">NandGame</a>: Build a computer from scratch.</li>
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<li><a href="https://boredzebra.com/100jumps/">100 Jumps</a>: Self-explanatory.</li>
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<li><a href="https://rose.systems/animalist/">List Animals Until Failure</a>: Self-explanatory.</li>
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<li><a href="https://backofyourhand.com/">Back of Your Hand</a>: How well do you know your neighborhood?</li>
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<li><a href="https://www.thewikigame.com/">The Wiki Game</a>: Click from one random Wikipedia article to another.</li>
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</ul>
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</article>
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</main>
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<footer>
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<p id="copyright">© 2026 filifa. This page is licensed under <a href="https://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA 4.0</a>.</p>
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</footer>
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</body>
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</html>
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@@ -29,6 +29,7 @@
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<p>Even worse, it's mostly stuff for <em>computer dweebs</em>. :((</p>
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<ul>
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<li>If you're just bored, <a href="bored.html">see here</a>.</li>
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<li>If you like trivia, try this <a href='mgs/mgs.html'>Metal Gear Solid trivia game I made</a>.</li>
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<li>If you're a computer dweeb, take a look at <a href="https://scm.dairydemon.net">my software forge</a>.</li>
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@@ -20,6 +20,7 @@
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<hgroup>
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<h1>Sums of Powers</h1>
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<p>Posted <time datetime="2026-04-15">April 15, 2026</time></p>
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<p>Updated <time datetime="2026-06-10">June 10, 2026</time></p>
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</hgroup>
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<p>This page is all about how we can efficiently compute large sums of
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@@ -402,7 +403,7 @@
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<p>This algorithm is quadratic in the value of
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<math><mi>p</mi></math>, which isn't great, but it's simple to
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implement (and I don't know of any faster way).</p>
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implement.<sup>1</sup></p>
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<section>
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<h4>Stirling numbers calculator</h4>
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@@ -460,7 +461,7 @@
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<p>It turns out there is a very elegant identity relating
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exponents, Stirling numbers, and falling
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factorials:<sup>1</sup></p>
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factorials:<sup>2</sup></p>
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<div class="math-block">
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<math display="block">
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<mrow>
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@@ -836,8 +837,8 @@
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</math>
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</div>
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<p>(For <math><mi>p</mi><mo>=</mo><mn>0</mn></math>, the sum is
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just <math><mi>n</mi></math>.)<sup>2</sup> This lets us
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simplify.<sup>3</sup></p>
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just <math><mi>n</mi></math>.)<sup>3</sup> This lets us
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simplify.<sup>4</sup></p>
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<div class="math-block">
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<math display="block">
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@@ -1057,13 +1058,21 @@
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<section>
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<h2>Footnotes</h2>
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<ol id="footnote-list">
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<li><sup>1</sup> For proofs of this identity, see chapter 1.9 of
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<li><sup>1</sup> I think we can technically compute all the Stirling
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numbers we need in linearithmic time by applying the convolution
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theorem to the numbers' explicit sum formula, but that approach
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makes it difficult to get exact values. If you just want the
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Stirling numbers modulo a prime, you could maybe use a
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<a href="https://en.wikipedia.org/wiki/Discrete_Fourier_transform_over_a_ring">number-theoretic transform</a>,
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but that's well outside my wheelhouse so I'm not going to touch
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on that here.</li>
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<li><sup>2</sup> For proofs of this identity, see chapter 1.9 of
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<cite>Enumerative Combinatorics</cite> by Stanley and chapter 6.1
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of <cite>Concrete Mathematics</cite> by Graham, Knuth, and
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Patashnik.</li>
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<li><sup>2</sup> See chapter 2.6 of <cite>Concrete
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<li><sup>3</sup> See chapter 2.6 of <cite>Concrete
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Mathematics</cite> for an explanation of this identity.</li>
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<li><sup>3</sup> A version of this formula is also mentioned in
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<li><sup>4</sup> A version of this formula is also mentioned in
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chapter 6.5 of <cite>Concrete Mathematics</cite>.</li>
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</ol>
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</section>
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