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It seems I created a meme

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Back in July 2005 I became intrigued with crafting weird and improbable magical items for the amusement of my Dungeons and Dragons gaming group. At the time, I had also been employed in the defense industry for about half my life, working around various weapons systems. Naturally, these things came together in creating a couple of D&D weapons, one of which became a meme in both D&D and in engineering circles . It started like this. Gary, one of the other players in our group, sent out an email to the other players warning about a possible dirty trick that Ian (our Dungeon Master) might play on those of us playing characters who rely on magic and magical items: Conventional D&D wisdom states that placing a rod of cancellation into a bag of holding, handy haversack, or portable hole will destroy both items in a massive explosion. I dunno if Ian is going to spring this to annoy folks who are carrying too much equipment, but you may want to store unidentified wands outs...
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My favorite mathematical card trick

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I learned this card trick in the fourth grade, decades ago, before the World Wide Web existed. I have never seen it written about, and anyone to whom I have shown it has never seen it either. This is surprising given how long I've known this trick. Did a brilliant classmate (or a parent) invent it? I'd love to know the origin. This is a mathematical card trick. Meaning, there is no sleight of hand, no actual trickery, just manipulation of playing cards that gives a surprising, final result. You can find many examples of mathematical card tricks on the internet; some of them appear downright magical and quite impressive. What the audience sees Here is how this trick appears to the audience. It looks like many steps, but they are easy to remember after you've practiced the trick even once: Starting with a deck of 52 cards (no jokers), you ask a volunteer from your audience shuffle the deck. You deal out the cards into seemingly arbitrary face-up piles, handing t...
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Legitimate uses of loaded dice

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A game master / dungeon master (DM) should never allow a player to bring 3D printed dice to a game. However, a DM could supply them to players, for certain purposes. In this article I examine the characteristics of "most fair" and "most unfair" designs of d20 dice, which I made in a CAD program and 3D printed for experiments. A fair and balanced d20 (white), a d20 biased to 20 (bronze, with the ☺ on the 20 face), and a d20 biased to 1 (purple, with the F for "fail" on the 1 face). A d20 is a twenty-sided icosahedron with faces numbered from 1 to 20. In the game Dungeons and Dragons , the d20 is ubiquitous. It determines success or failure of an action. It is the first thing rolled any time a player takes an action. The result of the d20 roll, with some modifiers added based on the player's character abilities and skills, determines whether the player's action succeeds or fails, with appropriate consequences. Advantage and disadvantage...
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Mechanical T flip flop counter in Minecraft

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My son and I began playing Minecraft together, me on my Windows laptop and him on his iPad. In my opinion, Minecraft is probably the only game in which a parent and child can play together in the same virtual world and both of them enjoy it. Quality time with your child in a video game? Who would have thought? The game is easy enough for a child to understand and complex enough for an adult to appreciate. In "creative" mode, it's like a giant Lego virtual 3D world in which you can build fantastic structures more easily than with Lego. Then there's "survival" mode, in which you're plunked down in a world with nothing, and you must gather resources, make your own tools, feed yourself, and so on — pulling yourself up by your bootstraps in a world full of both friendly and hostile creatures. One of the more intriguing features of Minecraft is the redstone circuit capability. You can build moving machines, logic circuits, devices that get triggered from ...
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A hypercube full of rooms

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While I'm on the subject of Dungeons & Dragons (see my previous post on ability score probabilities ), I recall something I did involving a tesseract way back in 2007 and posted on the community forum of Wizards of the Coast. WOTC took down their forum in 2015, but fortunately the Wayback Machine has an archived copy. Imagine a cubical room. It has four walls, a ceiling, and a floor (six faces). Each face has a door or opening, to allow you to pass through to the next room. Each cubical room connects to six other rooms — but there are eight rooms interconnected this way. This isn't possible to draw in 3 dimensions without distorting some of the rooms. Imagine a central room with a room connected to each face. So you have the center room, the north, south, east, and west rooms, and the top and bottom rooms. That takes care of seven rooms. The eighth room, we'll call it the "outer" room, is connected to those six rooms surrounding the center. Designating th...
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Most probable array of D&D ability scores

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There's an element to the game Dungeons & Dragons that lends itself to a numerical analysis: the initial array of ability scores assigned to a character. Some background: A character in the game has scores assigned to each of six abilities (strength, dexterity, constitution, intelligence, wisdom, and charisma). The first step in creating a character is to generate an array of six numbers by rolling dice, using a method known as "4d6 drop lowest". This means, roll four six-sided dice, remove the lowest value, then add the remaining three dice together (the result ranges from 3 to 18). Do this six times to generate an array of six values, then assign these values to your character's abilities as appropriate for the character's role (fighter, cleric, wizard, etc.). The problem The question I want to answer here is: What does a "typical" array look like? More importantly, how would I know if the array I end up with is better or worse than average? ...
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Syncing Office 365 Outlook to Google calendar using Power Automate

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When my employer switched over from the Google office suite to Microsoft's Office 365, it caused unexpected disruption in my family. I had been sharing my work calendar with my wife (sharing no details, just busy times). It became an integral part of her calendar, to help her coordinate (between her job and my job) who picks up and drops off my son from school, and to let her know when I was free to take a phone call during my work day. Since the switchover to O365, my ability to share a calendar externally was eliminated. Based on documentation I could find, it should be possible, but the option doesn't appear in my employer's implementation of Outlook. I can view my personal Google calendar in my work Outlook calendar, but I can't share it the other way. Microsoft's Power Automate provides a way to solve this problem. It lets you create flows of data, triggered manually or automatically by events, to move data around, not only among the Microsoft products but ...
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Whose hands are biggest? You may be surprised.

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A recent project to create an ergonomic handle for 3D printing led me down a path that introduced me to anthropometric measurements of the human hand, which in turn revealed some interesting facts about hand sizes. I had no idea that hand size is dependent on nationality, but I found a number of research articles on this topic. For those who don't want to read further, the answer to the title question is: Based on the data found, Filipino males have the biggest hands, by a significant margin. In fact, the margin is large enough that this population may be considered an outlier from the general human population with respect to hand size. Even Filipina females have larger hands than most males of other nationalities. On the other end of the spectrum, Vietnamese females and Indian females have the smallest hands. Now you can read on for the whole story, or you can skip down to the chart at the end. Idea for a toy My unintentional investigation into hand sizes started while de...
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Elliptical-blade NACA airfoil propeller

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You don't see aircraft with elliptical wings anymore. The most famous aircfaft with such wings is probably the Supermarine Spitfire fighter aircraft from World War II. Elliptical wings have the most uniform theoretical distribution of lift and therefore the least induced drag. In the case of the Spitfire, the gentle taper of the ellipse near the wing root also provided more room to mount weapons internally than a straight-taper wing, while providing an overall thinner, low-drag cross-section. However, with all curved edges, elliptical wings are expensive to construct. Of all the kinds of drag that a wing or propeller blade experiences, induced drag is an unavoidable price for lift. Induced drag has nothing to do with the drag created by surface area, surface roughness, or thickness of the airfoil. Induced drag depends on the planform shape of the wing. It is also inversely proportional to aspect ratio (the ratio of wing length to airfoil average chord length). The optimal and ...
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