The Sphinx's Lair

hm where's my puzzle, Sphinx?

Q: I have no idea what this means

2:03 AM

Hmm? What's this? A room. Great. Great. As if the guards don't know I'm claustrophobic. There's a strange text on the wall: Ribna tifmagta resru, sunte no, renler sludted dtednsehnun rurdal slutakdal danrtin. Hernite ridthet hori liridslu rtinrte. Ratslan tem netite nandethem. Themfmaglruhe toh...

enigmatic-puzzle story

@merrybot I got to an image. Can you please provide a text transcription of that image? Transcribing this whole thing seems horribly tedious. (Also, why edit to make it harder? The original version of the post is visible.)

@Deusovi oh pfft. um ok sure

edit: yes it is

> horribly tedious

even for me... (oh and can you find the one true part in the puzzle?)

I have no idea what you mean by the "one true part".

find the one part of the puzzle that is actually true. should be rather easy

Uh. "It is accompanied by another cryptic text" seems like a true sentence, and not just part of the story of the puzzle.

2:13 AM

umm no

but technically you're right

I'm not sure what you mean by "actually true" then.

>! first paragraph

oh uh that worked~

Q: A generalization of the lights-out problem

Look here for the original problem. Let the set $J$ be the set of pairs of positive integers $(m,n)$ with $m\ge n$. Suppose $(m,n)\in J$. Then there are $m$ lights, which they are initially off. Every step you choose $n$ lights, and you change their states. Let $f:J\rightarrow\mathbb{N}$ be a f...

mathematics lights-out

1 hour later…

oAlt

3:28 AM

@merrybot there is always a delay between the puzzle being posted and sphinx showing it here, lol

4:05 AM

Is every three-state Lights Out solvable for any n x n board?

Maybe this is worthy of a puzzling.se question?

A 4×4 board is not solvable with at least one configuration, no matter how many states you have.

(Same for other sizes too, 4×4 is just easiest to see.)

You can form an n²-by-n² system of equations in ℤ[n]: the independent variables are how many times each button is pressed, and then you can add all the buttons that affect a specific light.

Like, your first equation is "R1C1_presses + R1C2_presses + R2C1_presses + R1C1_initial_state = R1C1_final_state".

So, solving a Lights Out board is just solving this system of linear equations.

4:24 AM

interesting

For a 4×4 grid, the resulting 16×16 matrix is not invertible. (Press buttons OXOO/OOOX/XOOO/OOXO to get a +1 to every cell; then press the buttons mirroring those k-1 times, where k is your number of states.) That is, there's at least one way to get back to the starting state, besides just "push some buttons k times". So there aren't as many reachable states as there are total states.

what about 2 states? is every n x n 2-state Lights Out solvable?

That proof works for 2 states as well.

so for other states some configurations are impossible?

Yeah - on a 4x4 board, no mater how many states you have, you will always have some impossible states.

Here's another way to think about it: Every Lights Out board can be read as "instructions" for pushing buttons on a different Lights Out board. A button in state 0 means "don't press this", a button in state 1 means "press this", and if you have more states, a button in state 2 or 3 or whatever means "press this one this many times".

The result you get has no obvious relation to the instructions you used to get there, and it's not particularly helpful. But it's a thing you could do.

This gives you all possible sets of instructions, since order does not matter, and pushing a button more times than you have states just cycles things around.

(For instance, in 3-state Lights Out, the only options you have are, for each button, "push 0 times", "push 1 time", and "push twice"; any other thing you do to a button is the same as one of those three, and it doesn't matter the order you push things in.)

So, there are exactly as many possible "instructions" as there are configurations of a board.

4:31 AM

interesting

if the n x n 3-state Lights Out is solvable, would the Chasing Lights method still work?

On the 4×4 board, the OXYO/YOOX/XOOY/OYXO instruction gets you back to the start (where X is "push once" and Y is "push n-1 times"). Therefore there must be a board without an instruction leading to it: that is, a board that cannot be solved.

Chasing Lights?

Oh, just looked it up. Yeah, sure.

huh, thank you so much!

1 hour later…

Q: Mensa Finland IQ Test puzzle 34 Help

5:53 AM

I need help solving this ravens matrix Today I was going through the Mensa Finland IQ test and I came across this puzzle: After finishing the test the first time i came back to the question and struggled to find a logical way to solve it. 30 minutes later i decided to test which answer was co...

progressive-matrix

5 hours later…

10:27 AM

Q: What is a Limited Word™

This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles. If a word conforms to a special rule, I call it a Limited Word™. Use the examples below to find the rule. $$ % set Title text. (spaces around the text ARE important;...

pattern word-property

Q: Can we use only arithmetic operator to make this true

10:50 AM

Can we use only arithmetic operators (no digits) to make this true? 11 11 11 = 6

mathematics

11:36 AM

Q: This day in history IV

I haven't done one of these for almost a year and I'm planning to continue this. The correct answer to This day in history III was found by Mordechai (who just beat Tahel to it). On this date (03/05/2020), a certain amount of years ago, some sort of event happened. What was it and how many years...

riddle history

2 hours later…

Q: A phonetic Vowelburger™ Riddle

1:53 PM

You can find the other Vowelburger™ Riddle here I ordered 5 Vowelburgers™ with buns and meat only at the linguistic restaurant - help me identify each one from the description on the menu! The buns are pulmonic consonants and the meat is a vowel so the transcription of the Vowelburgers™ may n...

word wordplay language english

Q: To Sir(s): A Grandpa Tribute

2:16 PM

I found this paper on Grandpa's desk. Seemed like a tribute to me. His mediocre poetry notwithstanding, it seemed interesting with many familiar words. To Sir(s) Eyes on the target, finger on the gun Let me tell you again, it was twice as much fun Kill or die, the end came too ...

riddle knowledge

3 hours later…

Q: whether an element present in a sequence 2^n -1 or not

4:56 PM

How to check whether any element of the sequence 7,15,31,63,127... present in a range l to r, if yes than print that element of the sequence. if no than print -1.

logical-deduction

2 hours later…

6:28 PM

Q: Just a bunch of dudes too

A word was clued, then split into three fixes, which three other dudes clued. The clues are: I'm a sailor dude, I'm a generic dude, I'm an original dude, I'm needed for a road trip. Inspired by Just a bunch of dudes

riddle word

Q: Splitting a road trip into four

6:51 PM

A word is clued, and four parts of it (in order, but possibly overlapping) are also clued. The five clues are: I'm not for hands. I'm on this site. I'm full of anger. I'm full of anger. I'm used on road trips. What is the word?

riddle word wordplay

7:14 PM

Q: Simple: Find the code

Find the numerical code from the images. You don't get any hints.

mathematics