Yup. It’s the exact same phenomenon, just viewed through this tile-coloring lens.
(Though no one should let that intimidate them; I promise, the explanation for what’s going on here is head-slappingly simple)
(Or, just as well, playing on an ordinary flat board, but interpreting the empty space around its border to be one further giant tile, to be assigned a color as well.)
Your could also properly add two of the following three words to the list: TIME, DREAMS, CANADA
Not a lot of new puzzles came up this time other than the “which word doesn’t belong” stuff. (The current unsolved one was kind of relevant for the weekend, in a way.)
We spent most of the conundrums part of the day trying to figure out **septimus **'cryptogram and talking about some of the other puzzles in this thread. Thanks everyone!
Luxury - the others are titles of poems when “Ode to” precedes them
With all the hints Indistinguishable has shared about his coloring puzzle , let me try to connect the final dots.
[SPOILER]Hint 1: Given a tile and its neighbors in the plane, the central tile’s color can be changed without affecting the score. This is easily shown by just considering the transitions and observing they must balance. Since an all-green coloring scores zero, Hint 1 leads directly to the observation that all colorings of the sphere score 0.
Any finite tiling without holes on the plane is equivalent to a tiling on the sphere with one hole. The tiling’s score will be the negative of the score of the hole – the removed tile with its neighbors (i.e. the edge tiles of the planar tiling). Q.E.D.[/SPOILER]
Feedback would be nice. Please tell the puzzler if his was too sadistically difficult. (Indistinguishable got my cryptogram, but he didn’t say which of my hints he needed.)
(My own ignorances meant I never had a chance on the earlier word puzzles, though I’ll spend some more time on your latest Which doesn’t belong?)
There actually is a company called Ode to Luxury. However, this is not the answer to the puzzle. No poetry was used in the creation of the riddle.
The cryptogram was fair. My sister said later she had actually thought of a cryptogram, but dismissed the idea. But the quote was famous and known by everyone. Sadistic and difficult are great as long as the riddle is fair.
Some consider googling to be cheating, but sometimes that is the only way to get the answer unless you are in a group where people can throw out suggestions and determine the answer from the “hot or cold” responses from the one posing the riddle. I personally think googling just adds a new dimension to puzzle creation. To be fair AND have an answer not easily googleable is a challenge to the deviser of the riddle.
My sister had no idea about Greek prefixes, but Chronos’ “Dry, wooden…” problem was an excellent googling challenge. One just had to figure out what to google.
Word and logic puzzles work better for a live group than number or spatial riddles that require pencil and paper.
But I have enjoyed working on most of the puzzles in this thread. I do not think any have been impossible.
Honestly, I was amazed that that one wasn’t Googlable. I didn’t expect to see it as a puzzle, but I would have thought that one of those Word Maven-type blogs would have done an article on why there are so few words starting with X, and saying that they all came from Greek roots for…
Company, but not poem.
Fair enough, **Knowed Out **. Googling I also find an Ode to Canada, an Ode to Time and also an Ode to Dreams. There seem to be loads of odes. Good answer then, but not the one that inspired the riddle.
There is even an Ode to “HATRED.” That word also could have been in the original list, but it is such a negative word I chose not to include it.
There is an Ode to “LOVE” as well. Several, in fact. Very positive word, love. But LOVE would not fit the list.
Well done! The way I think of it is like this:
Given a transition between adjacent tiles T -> S, let’s say it’s worth +$1/3 if its colors are red->green, green->blue, or blue->red, worth -$1/3 for the reverses of these (red->blue, blue->green, or green->red), and otherwise worthless. [Actually, all that really matters is that the red->green, green->blue, and blue->red worths sum to $1, and that reversing the direction of a transition negates its worth; this is just the nicest way to do that]
Note that our basic scoring rule is equivalent to saying that one earns, at every point where three tiles meet, the cumulative worth of the three clockwise transitions around that point. [RGB comes out to a total of +$1, the opposite RBG comes out to the opposite -$1; anything else is either three of the same color (worthless), or two of the same color then transitioning into and out of a second color (those two transitions cancelling out in worth)].
But note also that, when two tiles meet, they meet along an arc between two endpoints, and moving clockwise around one endpoint transitions between the two tiles in the opposite order as moving clockwise around the other endpoint.
Thus, almost every transition earning or losing anything is cancelled out by an opposite transition.
The only exception is the transitions between the tiles at the very outside border; here, when two tiles meet, one of the endpoints of the arc along which they meet is on the outside border and thus is not used in scoring (touching only two tiles and the outside world, instead of three tiles).
Thus, the total profit of a board is due entirely to the transitions between the colors on the outside border. The profit is simply the sum of these transitions in clockwise order.
[For a closed spherical shape like a cube, tetrahedron, soccer ball, or flat board with the outside world considered as just one more tile, things are even simpler: there are no exceptions, every scoring transition is cancelled out by an opposite one, and you must break exactly even]
Note that the above also lets us extend the phenomenon to boards where more than three tiles may meet at a point, using an appropriate profit rule for such points.
There are also analogues in any number of dimensions, and all sorts of other generalizations, but 2d boards with 3 colors seemed the sweet spot for a simple puzzle. 
(I was motivated to pose this puzzle, incidentally, as the next in a sequence of riddles in the thread at the time whose punchlines all amounted to “It seems complicated, but it hardly matters what choices are made; the result barely depends on it”.)
I read every hint posted in the thread before my answer, so I can’t empirically claim any of them were unnecessary, but it seemed to me the only one that actually mattered to my thought process was the very last one you posted, “Anagram? No. Letter play? Yes.”.
Again, I’ll ask: is the answer criterion one which the average person would immediately recognize all these words but one as matching, or one where the average person would have to consult some reference to determine what fits and what doesn’t?
Following up on this:
I shouldn’t have bothered saying 'spherical", because the sphericality doesn’t matter, just the lack of a border; playing on a torus, for example, would similarly necessarily result in breaking even.
Unlike a previous riddle, I do not think most people would know the words in this riddle match the criteria. Certain professionals and a few amateurs would.
In the top twenty-five tallest peaks in the U.S. riddle, certain words or names would have given it away. Elbert, Foraker, or Saint Elias would have all led to a quick and easy solution. So I had to choose words that fit the criteria but didn’t instantly scream “Mountain!”
Here, I have posted many of the words from a certain list, but the connection of those words to the common factor may require a bit of looking up or googling. I am not sure any one word from the list could lead to the answer instantly. I did hope that including a false word would make discovery via googling a bit harder.
Odd that looking around for the list of secret service codenames took only a googling moment for solvers, but this common factor is harder to find. I hope these hints will help —without spoiling the riddle by giving it away immediately.
In that spirit, here’s my own puzzle:
BLOODY, REDDISH, LOUSY, DRIED, SMALLER, LONGEST, DRUNK, BURNT, TORN, ASHEN, NOSY, DOGGED, MOUNTAINOUS, FISHY, SLEEPY, BITTEN, STONED
Which word doesn’t belong?
Got to remember. Always read the small print.
Heh heh.
Answer:
Dogged.
All other words could describe a different GOP presidential candidate.