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Tuesday Teaser #54: Jewel-Encrusted Patchwork

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I apologize for being late again. I should have remembered that I lose connectivity late at night, but even forgetting that, I should have done all the work earlier. But in any case, here's the first puzzle in this misordered series of pony tributes, a cryptic Shakashaka for Rarity.
Generosity photo Generosity.png
Colors, as usual, are courtesy of the Kinky Turtle. The rules are as follows.

Your aim is to shade in a number of half-cell triangles so that the remaining white space forms a number of rectangles, many tilted at 45 degrees to the grid, that share no edge. Rectangles may touch corner-to-corner or corner-to edge. Triangles may touch anywhere. (As a solving aid, each square cell is divided into quarters. If any part of a given cell is shaded, it is exactly two adjacent quarters.)

Each letter represents a distinct digit from 0 to 4, inclusive. This clue number is the count of black triangles that are to share an edge with that clue's cell in the solution. The meaning of each letter is for you to determine.

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Tuesday Teaser #53: Square Dance

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Well, shoot. It ain't ideal, but it's still Tuesday in Alaska.
Honesty photo 1394003967.jpg
This here puzzle's a cryptic variant on Country Road. Whatcha need to do is draw a non-crossing loop from square to edge-adjacent square so's there's one segment in each outlined region.

Two provisos there. First, y'all don't need to visit every square, but where two squares share a thick border, ya gotta visit one or both. An' second, those letters represent numbers, cryptogram-style, an' those numbers are the number of squares in that respective region's segment.

There ya go, third pony puzzle on the LiveJournal. Ah figger ah'll put Rarity's up next week, just fer completeness' sake. Yee-freakin'-haw!

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Weekend Update

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My mom informed me a week or two ago that I have a worldwide fan club. So I figured I should post something for all of you. This isn't exactly that post.

I haven't exactly had a packed schedule the last three months. The garage door is now half-insulated; I gotta finish that. I have get-togethers away from the house on Sundays and Tuesdays, though that's a little up in the air right now. I've also been keeping up with MLP, and even now, I'm lining up an Applejack puzzle for Tuesday.

Now if you'll bear with me a minute, I'm gonna chase that last bit around. Those of you who've been watching, or otherwise keeping track of, the show, know that the six central characters (known to fans as the "Mane Six") have been, one by one, finding special objects that display rainbow shimmers to the camera. I won't discuss the important details here; I just wanted to note that the first three ponies to find their object were also the first three I made puzzles for, which only had one chance in ten of happening. And I say 1/10 instead of 1/120 for two reasons:

A) because I got the order wrong, so it was six times as likely that I'd match three ponies, and
B) because come on, Twilight's obviously going to be the last one in both lists, so I only really needed to arrange five ponies. (Which, see point A, I didn't do quite right.)

Anyway, I replaced the image for Rainbow Dash's puzzle because some grid lines had been lost to artifacting. And speaking of things I've lost, I had a puzzle written for Fluttershy, but it was... unkind, so to speak. The answer grid was all right, but I wasn't sure how to solve it or how many extra clues to give. Then I put it off so long, I lost the notebook I'd put it in. >(\< So that won't be up for a while, though I'll probably include Rarity's puzzle for completeness, with a color adjustment.

And that's really it for now. See you Tuesday!

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Tuesday Teaser #52: Zag

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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.
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(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.)

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Tuesday Teaser #51: Blatant Self-Insert

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I blew past midnight a little. Briefly, the inside edge of this tapa is continuous with its outside edge. Each square counts as 1. Don't completely surround any one corner.

Inside-Outside Tapa photo BlatantSelf-Insert.gif

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Tuesday Teaser #50: Vanity Racecourse

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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.

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We are the coins in the Potter's purse

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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

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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.

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Tuesday Teaser #49: Bag of Tricks

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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.

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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.

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