The Sphinx's Lair

1:31 AM

I am stuck :(

also stuck

I think it's supposed to say PSE though

Q: Double Chocolate: Happy Valentine's Day!

Hikouki (@flight_float) over on Twitter issued a challenge to make a Double Chocolate logic puzzle with a fixed grid pattern, and lots of logic puzzle makers responded to that challenge! Here's my take on it. Rules of Double Chocolate: Divide the grid into regions by drawing along some ...

logical-deduction grid-deduction

1:54 AM

@Avi seems like you made an incorrect deduction at some point

I solved it

(the puzzle can be solved purely logically - no need for any guessing!)

but not posting the answer here directly

the 4 group at the top there is incorrect

start with 14 that has to be the same shape

you get the 1 on the bottom and the 1 on the bottom right for free

with some brute force the top left can be completely solved

then the pentomino pattern is the only option for the top center

ew, brute force

the 1 can go to the bottom or the right

and you need to show that the 2 doesn't go under the 1

which means that the 4 would be misshapen and cut off everything

that's the "brute force"

hence, the 1 has to go down, the 2s are Ls, and the 4 is a double-L

the 1 on the top right has only 1 choice

combined with the S you get the 4

which has neighboring squares that must connect to the white section on the bottom right corner

because the 4 must be a double-L, otherwise it will cut off the entire bottom right side

from that point the 2 is obvious, and the puzzle is solved

as for solving speed, I didn't notice the 14 for a while so I just messed around on the top

also, i posted images of the struggle instead of actually solving lol

Dark elf opining wildly: "Oi! Get out! It is a place for killing!" (8,3)

DROW + (-oi)NINGP* + IT = DROWNING PIT [a place for killing]

2:16 AM

Currently trying to write up an explanation for the Double Choco. Even though it's a very intuitive deduction, I can't seem to rigorously prove that the 14 region must be like in the solution

#mathmajorproblems

well

you see

there is only 1 group of white squares it can be connected to

therefore the shape of the other region must be equal to that shape of squares

because the group of white squares is can be connected to, is exactly 14 squares

and seeing the 5-edge 4-edge

there's only 1 way it can be flipped

not possible for it to be any other way

there's no proof, really - it's just the rules of the puzzle that all regions must have the same shape

@Avi That's not immediately obvious though. What prevents that region from connecting to the group of white squares on the top or the right of the grid?

I'm like 99% certain this was intentional

the top?

if you connect it there

the forced square for 1

means that you will always infringe on the right of 4 to access white squares

also, there's no other way for white to connect to the board on the bottom right

in a way that allows 14 to connect to another group of white squares

actually there is

but then the stringy noodle shape 14

will not fit on the right side either

as it will also impinge on 4's access to white squares

Yeah, I just realized that if we tried to force the 14 to connect to the top or right, then we cannot complete the other numbered regions anymore

it's specifically the 4

on the top right

because reaching the white right side

requires 8 in a row

8 in a row will always block the access for the 4

2:28 AM

The 4*s* actually, since we could have a 14 region in the bottom right that frees up the upper 4, but not the bottom 4

remember, they have to be the same shape

oh, actually, you're right

I'm not talking about shapes cause that's too difficult

Size is what's important

ok so basically

it can come across the top as a straight line to the right

or it can zig-zag down to the bottom

or it can elbow down to the bottom

the first of those covers the top 4, the second covers the bottom 4, and the last of those I can't disprove mentally

@Avi That would still cover the bottom 4

Yeah, the elbow has to be fleshed out

because there are no more black squares

and the 5x5 elbow isn't 14 squares

only 9

so going down to the bottom covers the bottom 4

going over to the right covers the top 4

going over to the top covers the top 4

3:18 AM

@Avi it wasn't

2 hours later…

5:21 AM

7 hours later…

11:56 AM

Q: I am musical in function

My prefix can fool you Even though it’s not a pro My infix is a pipe Through which fluids flow My postfix: a conjunction But more of a disjunction I have no intersection I am musical in function

riddle word wordplay rhyme poetry

Q: Rotating numbers in a 2x3 grid

12:37 PM

We have a 2x3 grid numbers like so 6 5 4 3 2 1 Four numbers in any 2x2 sub-grid can be rotated clockwise or anti-clockwise. For example a b c d rotated clockwise becomes c a d b What is the fewest number of such rotations required to obtain the following grid? 1 2 3 4 5 6

mathematics combinatorics

Q: Rotating numbers in a 3x3 grid

1:17 PM

We have a 3x3 grid numbers like so 9 8 7 6 5 4 3 2 1 Four numbers in any 2x2 sub-grid can be rotated clockwise or anti-clockwise. For example a b c d rotated clockwise becomes c a d b What is the fewest number of rotations required to obtain the following grid? You may need a computer for t...

mathematics combinatorics computer-science

9 hours later…