Tuesday Teaser #52: Zag

I seem to have a tiny dilemma here. I actually had this puzzle written last week, but Tuesdays are now host to "Agents of SHIELD" viewing parties. And sure, I should post these in the morning, but I'm not generally a morning person. So should I move my weekly (ha) puzzle to another day of the week?

Anyway, here's a sudoku variant called X-Sums Sudoku, which I first saw on Para's site (http://puzzleparasite.blogspot.com/). Each outside clue equals the sum of the first X digits in its line starting from the edge where the clue is located, where X equals the nearest such digit.
 photo X-SumsSudokuZag.gif

(Not to be confused with N-Sums sudoku, where N is the last of the N digits to be added. That, incidentally, means not all 36 spots around the grid can have a clue.)

Tuesday Teaser #50: Vanity Racecourse

Heyo! I'm alive and not only buying pony pictures, but also writing pony puzzles! Here's number 3 of 6, a halfway point for a half-century mark. (Oh, I don't mean me. I only turned 27 last month.)
RD Vanity Course photo Loyalty.gif
This puzzle type is called "Slalom," and it's probably the best thematic fit so far, a race-themed puzzle for a pony who loves to go fast. Composition was a pain, though. (Had to get it just perfect.)

The object is to draw a loop that goes from square to edge-adjacent square, starting and ending at the checkered square and crossing every hurdle once in order. "Crossing" means starting on one side of a hurdle, taking two consecutive steps perpendicular to it, and ending up on the other side of the hurdle. There are 26 hurdles here, labeled A-Z; ten labels are shown here.

Normally, labels are numbers, and the number of hurdles is given on the equivalent of my checkered square. I felt all right giving the count outside--though actually, there's a little room for that under the grid if this way is too obtuse--because W is so close to the end of the alphabet, so it should be pretty obvious. Also, hurdles are traditionally bracketed on both ends by black blocks (which cannot be traveled over, in the vanishingly slim case that this wasn't guessed), but that obviously crowds grids and would have interfered with the tight theming.

Okay, that leaves AJ, Fluttershy, and Twilight. I can definitely get this done before the end of the TV series, no problem.

We are the coins in the Potter's purse

Hey. Not much in the way of written puzzles, certainly not enough for a Tuesday Teaser, but I did gander at the galleon-sickle-knut currency system of the Harry Potter world. Seems a galleon resembles a hubcap of solid gold, weighing as much as eight dinner buffet plates, so it probably wouldn't be carried around in a typical coin purse.

Anyway, there are 17 sickles to the galleon and 29 knuts to the sickle. Naturally--well, enough for a recreational mathematician--I wondered if there were amounts of money which, when doubled, transposed the numbers of each coin type. Short answer, yes.

First, a ground rule. Just like you wouldn't say something costs one dollar, two hundred ninety-nine cents, neither should the amounts of wizarding money be named with more than 16 sickles or 28 knuts. Alternatively phrased, an amount of money should always use a galleon when there's an option to use 17 sickles or 493 knuts, and a sickle when there could be 29 knuts.

So now I won't keep you waiting. There are three unit prices (I think), besides free, where the price of one and the price of two use the same numbers of coins in a different order. Find them.

Meandering philosophy

Funny thing, free will. The only way I've found to test it seems to be impossible.

The idea of free will is that an entity with it isn't fated to one choice vs. any other, right? They might have a preference for one or several options over others, and they might be open to outside persuasion, but that's no guarantee of their future decision. In short, a past decision where free will played a role could have gone another way.

The problem is there's no way to check that. We can speculate on past decisions, sure, and brainstorm about future decisions, but the number of possibilities we can actually observe is either 0 (before the point of decision) or 1 (after).

Even if we speculate a technology (or other method) by which we may view multiple universes, wherein one (initial) decision (semi-arbitrarily chosen to be interesting) was resolved several different ways, that doesn't prove any involvement of free will. Heck, this scenario constructs an infinitely-branching (perhaps even merging) multiverse wherein no timeline is more clearly valid than another (actually, that might be mistaken, but saying so necessitates a metaphysical mathematics I've never heard of); that is, if you don't even need free will to make all the decisions at once, you don't need free will for any one of them.

What's needed is a way to replay a timeline to check whether anyone behaves differently when they all start with perfectly identical memories and perfectly identical circumstances. But even then, there's no way to get completely outside and say that any resulting differences weren't fated.

I dunno. It's something I had to mull over. Maybe I can get some puzzles up this month.

Tuesday Teaser #49: Bag of Tricks

Okay, "next week" didn't work out. But here's a puzzle that just might be your bag!

Bag of Tricks
...Well, it would be if you are Pinkie Pie, and I can't really rule that out.

So this is a Bag puzzle. I'll admit I don't usually use the name "Bag," but I think it fits Pinkie better than "Cave" or "Corral" does. It's the second puzzle in a planned six-part series based on the core cast of "My Little Pony: Friendship is Magic." (Did I mention I'm a brony? Well, I am now!)

I had intended to do something with balloons, but I got inspired to do something typically mathy. I was able to arrange pi (3. 14 15 9) and e (2. 7 18) on the diagonal in Pinkie's mane and coat colors, so that spells "Pie." To read "Pinkie," take the numbers in colored squares from top to bottom, left to right. Reading the sixth row (colored like Pinkie's balloon cutie mark) in the common 1=A, 2=B fashion gives N, K, I, so all together it says "Pi{nki}e."

Some credit goes to kinkyturtle, whose colorkeying of Pinkie I used here. He links the current version here as he updates it. (Mostly I just want to point him out to you and this entry out to him.)

Wait, you're wondering how this is the *second* puzzle and not the first? Oh, right! The first puzzle is the second one here. Sorry, both writing and sending the puzzle were done on the spurs of their respective moments. I'm pretty proud of it, too; I managed to pick a puzzle type that's basically about finding diamonds and/or cutting cloth, so it's perfect for Rarity.

This means there can be a chimera of hybrids, but not vice versa

Yeah. So... yeah, I didn't have a Tuesday Teaser for New Year's Day. I've been alternately sick and working on the Mystery Hunt. And more recently... neither.

*sigh* I'll have something more substantial up in the coming week. But for now, a terminology note. I propose that "hybrid" and "chimera" not be strictly interchangeable.

With regard to furries, a hybrid should be an individual body (exact definition subject to twinning and conjoinment) with approximately blended features of two or more species, allowing for variegated expression of those species' individual features. A chimera is more of a Mr.-Potato-Head approach, with swaths of body being one species or another (or one genotype or another, but this is harder to make out). Multiple heads being distinct species is popular and supported by mythology.

With regard to puzzles, a single-grid puzzle would be a hybrid if the constituent genres' rules were used in tandem to arrive at a single solution. A chimera calls on each set of rules separately to arrive at independent solutions.

ETA: The puzzle Grant is talking about is here. And yes, that's where I got "chimera" from.


You'd think with how irregular my posting schedule is that it would take the end of the world for me to create a new puzzle. Well, you'd be wrong! I actually created this one this Tuesday afternoon. Okay, there's going to be an Internet glut today, but it's rarely a bad time for puzzles.

ETA:Oh dang it! Not only did the rash of apocalypse-themed puzzles not come, but I forgot to say what type this is! Anyway, it's a slitherlink. Draw a loop along the edges, a loop that doesn't reuse any edges or points, such that each number says how many sides of its square or triangle are used by the loop.


Hey, LiveJournal changed its posting interface. That's kinda interesting.
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Tuesday Teaser #47: Snub Fillomino

Ah-kay. So Palmer Mebane was able to write half of Fillomino-Fillia 2 while helping with the 2013 MIT Mystery Hunt. I, in a word, wasn't. I'm sorta writing a puzzle that might get its answer changed, and I'm not progressing on others, so I can't help but feel I'm doing it wrong.

Anyway, here's an idea I got while procrastinating on everything else. This Fillomino variant is based on the snub square tiling, and while you're solving, the triangles count exactly the same as the squares.

More explicitly: write a number in each square or triangular cell so that, starting at any cell and traveling only by crossing edges, only to cells containing the same number, you are able to reach that number of cells total. Alternatively, you can just darken some edges to separate shapes, making sure all pairs of shapes with a dark edge between them have different numbers of cells.

Snub Fillomino
(Any ideas on a better title than Snub Fillomino?)
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