I have no idea what I’m doing and you can’t stop me.

Author, Trans Woman, Hypno Domme, Hopeless Romantic, Sadist, newly out system.

Pronouns are She/It, perpetually happy HRT gave me titties and sad it didn’t give me tentacles.

I had shame once.

Ξ

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Dating: @lunasorcery

18+ only


lunasorcery
@lunasorcery

Puzzle:
Including reflections as unique solutions, how many ways can you tile a 2×N rectangle with dominoes?

Choose your adventure:
If you’d like to find joy in exploring for yourself, you can stop reading here; enjoy!
If you’d like to see the answer, along with a rough proof, click below.

show solution Let’s have Fn represent the number of tilings of a 2×N rectangle. We can see that F0 and F1 are both 1 — there’s only one way to tile a zero-width rectangle (with zero tiles), and only one way to tile a 2×1 rectangle (with one tile).

For larger rectangles, consider the following:

The end of a 2×N rectangle can be filled with dominoes in two ways — a vertically-oriented domino, or two horizontally-oriented dominoes.

If we place a domino vertically at the end of our 2×N rectangle, we’re left with a 2×(N-1) space, which can be filled Fn-1 ways.

Similarly, if we place a pair of dominoes horizontally at the end of our 2×N rectangle, we’re left with a 2×(N-2) space, which can be filled Fn-2 ways.

From this, we can conclude that Fn = Fn-1 + Fn-2, and with initial conditions of F0 = 1 and F1 = 1, this gives us the Fibonacci sequence!



tomotter
@tomotter

Species in this setting:
The People, from planet Dirt orbiting Star
The Us, from planet Rock orbiting Star
The People, from planet Planet orbiting Star
The Not-Animals, from planet Dirt orbiting Light
The People, from planet Dirt orbiting Star
The People, from planet Here orbiting Star
The We, from planet Ground orbiting Brightness
The Us, from planet Dirt orbiting Star


estrogen-and-spite
@estrogen-and-spite

Relevant excerpts from one of my books (The Dinosaur Dungeon). It's a fantasy setting, and most worlds nave true names so translation magic doesn't cause problems, but Earth lost its true name which is why people from other worlds hear it referred to as Dirt. There's an Earth native character in the story, a member of a guild of people who basically got to have portal fantasy adventures and then returned home, realized they didn't fit into society, so became adventurers going back out into the multiverse. Magic automatically translates the first language they hear upon arriving in a world, and telepathic communication bypasses linguistic barriers, but because Earth lacks true names for non sentient beings, a lot of oddities result. See also the Desert Desert, Desert Desert, and Desert Desert, as well as all the River Rivers.

Its hard talking to a Dirtworlder about their life sometimes.