[grid-deduction] Puzzle Solving

"we can't block yellow into being a rectangle
so either the snake ends in the yellow corner (yellow itself, or just above it), or the numbers aren't all the same (which implies that the snake ends in pink)"

the snake must end in the yellow corner if all the numbers are the same

meaning red and blue cells are nonsnakes

and if we have the other side of those bars as also nonsnakes, there is a problem because then the 1s don't see the same thing

bobble

but why must it end in yellow if all numbers are the same? wouldn't it have to end in yellow no matter what?

Deusovi

one sec let me try to reconstruct my logic from earlier

hm wait does it have to end there no matter what

yeah actually i think you're right - it will end in yellow corner no matter what

bobble

or it could just not go to yellow?

Deusovi

5:08 AM

no, that's not possible

say the snake visits neither R9C10 or R10C10

bobble

because either side of the line is different, and if different numbers then the 1s on either edge can't be same

Deusovi

right

bobble

and the same logic holds for all the other corner areas, so now we can place snake segments

Deusovi

so that means these are the two endpoints of our snake - somewhere in the left bit of circles, and somewhere in the right bit

bobble

you're missing a wall between R5C9 and R5C10

Deusovi

5:13 AM

oh am i

so i am

merrybot

(hey mith!)

Deusovi

bobble

also, R2C7 can't be snake, otherwise R1C6 or R2-3C8 is boxed off in a rectangle, so R1C6 is snake

Deusovi

ah you're right

bobble

you put updated wall in the wrong place - it's a vertical border

Deusovi

5:16 AM

...oh thanks

bobble

I added in the fs now, to prevent rectangles in that area. Can we say anything about the square I have my cursor on?

Deusovi

well it's not a snake

i think we can say this though - the two segments i have marked with an X are not used by the snake

bobble

I think that's all right? I was trying to see if I could declare it as either definitely part of or definitely not part of f

@Deusovi because Rectangle Is Bad

Deusovi

top one's pretty easy; bottom comes from...

yes that

Rectangle Is Bad

oh i see something

say region A (red) doesn't go right

it can be at most 6

because otherwise it squeezes the snake into touching itself

but we already know our corner number is bigger than 6, because otherwise blue would be a rectangle

bobble

why couldn't it be 8 and let the snake escape through R6?

Deusovi

5:22 AM

because where would the other end go

it would have to escape through R7, but then the snake would touch itself

bobble

I'm not entirely convinced that the lower X is true (probably should have mentioned this earlier)

oh wait I see why

Deusovi

yeah we can't make R8C1 not-a-rectangle if we use the lower X

bobble

okay, so red goes right then

Deusovi

so, current progress here (i've switched to your letters so it's easier)

merrybot

how in the world do you make those images

Deusovi

5:26 AM

(oh and F connects to both adjacent squares)

swaroopg92.github.io/penpa-edit

bobble

@Deusovi why?

Deusovi

uh you have F in all three squares there too

i just didn't mark it

oh my bad, i can see how that was ambiguous

bobble

Oh, I thought you were talking about R3-4C7

Deusovi

yeah my bad

ok so if D is the snake, E can't go through the lower X either (edit: no, it can, but it can't just go that way)

bobble

some stuff we know about the number the 1s can see:
C9 & C10 both must see >=7, so
R1 & R2 both must see >=7, so
C1 & C2 both must see >=7, so
R10 must see >= 7, so
R9 must see >=7

(I can explain the logic for any of those if needed)

Deusovi

5:32 AM

yeah, agreed

bobble

@Deusovi so e can extend rightwards? two?

Deusovi

bobble

and you just did that

Deusovi

yeah, E must extend at least two rightwards, or otherwise it makes R1C8 into a rectangle (or crushes the snake at the top)

hm, i think i've convinced myself that R10C7 can't be snake

bobble

I think we've passed the break-in stage, yes?

Deusovi

5:36 AM

probably?

why

were you just looking to do the break-in and then continue solo?

bobble

because the hint is only for break-in, so no more looking at the hints for help

Deusovi

ah yeah

bobble

which I was totally doing, but it wasn't helping

9 mins ago, by bobble

Oh, I thought you were talking about R3-4C7

still not sure why these are F

or are they not F, just non-snake?

Deusovi

they're not

green is "not snake"

yeah

ok i have successfully convinced myself that R10C7 cannot be a snake

bobble

I would love to hear this explanation

Deusovi

5:39 AM

if r10c7 is a snake we get all of that (lighter gray = snake, yellow = nonsnake)

and now we can't make B a nonrectangle and still reach one of the bottom-right targets

bobble

I agree with this, now what can be done with it?

(also I keep trying to convince myself that this is us collaborating, but really you're mostly solving while I ask for explanations)

Deusovi

...we can mark R10C7 as "not a snake"

i have no idea how this is helpful but it's information at least

(shh no that's not true)

bobble

mark R10C6 as "not a snake" while you're at it

oh wait but what if D is snake

aggh

Deusovi

oh?

yeah

Mithical

@bobble you have become a rubber duck. much luck and success in your newfound role

bobble

5:42 AM

can I be a rubber squishy crown instead?

Mithical

(en.m.wikipedia.org/wiki/Rubber_duck_debugging)

Bwahahaha, SE's April Fools thing made it in there

bobble

okay, so D is at least 5, right? because it has to be a non-rect. if it is 6 or greater, then it E has to either be the snake or 8 or greater, which I'm not sure will fit? maybe?

merrybot

@Mithical suddenly i want a rubber duck so it can help me debug stuff

Deusovi

hm, how will it not fit

if E is the snake it can go up-right-right-up-up, and i think that works

bobble

I'm about 12% sure that an 8 or greater won't fit

Mithical

5:47 AM

@merrybot James Vietch might have one to spare

bobble

I wasn't saying that E-as-snake wouldn't fit

(should this solving be split off into its own chatroom?)

Deusovi

well if D is 6+, E must be the snake

(yeah we could do that - i'll migrate)

← 126 messages moved from The Sphinx's Lair

alright here we go

bobble

something else useful (?) - R1C8 can't be snake, because it can't escape

Deusovi

R8C1, yeah - and R8C2 too

bobble

you can add more green squares to your pretty picture!

Deusovi

5:52 AM

probably makes sense to take out that X too

bobble

snake can't escape through the gap in R4, because then R2-3C4-5 can't prevent a rectangle

that's another X

Deusovi

ooh good catch

wait i'm actually not convinced there

bobble

and that X gives R6C4 as snake, because that's the only way to escape

Deusovi

why is this bad

bobble

oh I was pretending that the snake couldn't touch the R3 border

which is.. not true

Deusovi

5:57 AM

weird deduction: R5C3 not snake

because it would touch whatever path it isn't a part of

bobble

this is true!

Deusovi

i think it's absolutely useless

but true!

bobble

the two green spots near F have to be part of at least a 5, to prevent consecutive

how is this useful? shrugs

Deusovi

bobble

wait why is R1C7 not snake?

Deusovi

5:59 AM

R7C1?

bobble

oh because Rectangle Bad

Deusovi

yeah

bobble

and yes, R7C1

Bubbler

Looks interesting, what kind of puzzle is it?

Deusovi

oh boy

bobble

6:01 AM

in The Sphinx's Lair, 7 hours ago, by bobble

Deusovi

it's a snake no-rectangles non-consecutive skyscrapers borders fillomino

bobble

Fillomino, and then all of these variations

Deusovi

you know, a perfectly normal puzzle type

bobble

I'm also going to have to go to sleep really soon, so can this wait until tomorrow?

Deusovi

sure!

bobble

6:04 AM

I'll stay in here and stare at the puzzle until I have to leave - try to remember it well enough to solve in my sleep :D

matt

that is quite unlikely to happen, you know

:p

Deusovi

good luck!

(ooh r4c4 snake)

(and r6c2)

bobble

agreed on both counts

Deusovi

ooh wait progress

that means that the top segment can't escape by going down from r4c4

because then it would run into the bottom segment

so it must escape through row 4

bobble

and it must the R4 border on one side, and one side only, making A 8 and therefore a bunch of other stuff must be 8

and now I really have to leave - bye!

Deusovi

6:08 AM

aw see ya

(hm i'm not sure why it can't be 7)

bobble

4:10 PM

Yeah, I realized it could also be 7 as soon as I closed the computer :D

bobble

5:38 PM

I got a proof that if R5C9 is non-snake, then the snake can't escape down C8, because then g & b can't both be non-rect. Currently looking for a way to extend this logic to either rule out escaping down C8 entirely (and maybe C9), or rule out R5C9 as non-snake

(by which I mean declare R5C9 as snake)

Deusovi

why does g have to be non-snake?

oh wait

misread what you said

yeah that makes sense

bobble

extension of if-g-is-non-snake: also no escaping across R6, because then no room for the R1 & 2 snake

Deusovi

right

bobble

am I falling too far down a rabbit hole?

Deusovi

¯\_(ツ)_/¯

oh hold on i was missing that bar in C6

yeah with my "R10C7 can't be snake" thing that might help a lot

bobble

5:47 PM

Deusovi

bobble

further into the hole: e & c must be the endpoints, because there wouldn't be room any other way

Deusovi

sure i agree

bobble

I'm struggling to figure out how to make this useful, so I'll give up on this line of reasoning for now

Deusovi

hm we did figure out that the number for A/B must be either 7 or 8 though, right?

bobble

5:48 PM

yep, can't possibly be higher (no room) or lower (because B must be rect)

Deusovi

right

that seems useful

bobble

I think R8C3 must be non-snake, because if it is snake there is no way to fit the snake and a non-rect B and a non-rect R7C7 in

see any problems with this idea?

Deusovi

well we already figured out that neither of the two cells you've marked as snake on the bottom are snakes

so that's an easier route to a contradiction

bobble

oh yeah I hadn't marked them on my grid

but R8C3 = non-snake, right?

Deusovi

yeah i agree

bobble

5:58 PM

because e just doesn't have the space it needs

returns to staring at grid

Deusovi

i believe we can rule out R9C6 snake

because it would have to take that route immediately (before visiting the other corners), and then we couldn't get it back out to visit the others

bobble

processing

I agree

Deusovi

i also think we can rule out... R7C7 snake?

because it couldn't visit there near the end

and if it visited near the start we have too much crammed together again

bobble

6:14 PM

you're missing another border between R8C8 and R8C9

Deusovi

oh come on how did i not notice that

thank you

bobble

should make the ruling out easier?

bobble

6:42 PM

And I agree on R7C7

Deusovi

hm

if E is snake, can we fit a 7 region above it

bobble

anything wrong with this?

Deusovi

hm, no, i think you're right

i was thinking about that option but wasn't sure if it was bad

d would have to be 7, filling its entire bottom row segment as well as R9C6 -- but i don't think that leads us to any contradictions

bobble

could you post board updated with the new border & the latest non-snake square?

Deusovi

bobble

7:01 PM

I'm thinking that R7C3 is non-snake, because if it was snake that would force R8C3 into a rectangle. Any problems with this?

Deusovi

ooh yeah i think that's right

bobble

which means snake escapes through R6, so a bunch more snake squares

or, no, maybe through C4?

Deusovi

bobble

R6 snake must go down through either C4 or C6 to connect to E or D, yes?

Deusovi

yeah

bobble

7:05 PM

which means R6C7 is non-snake, so R5C7 is also non-snake

oh, wait, nope

Deusovi

hm i think that's actually true

because if you push things left like that, the snake will have to go to E

and then you can't fit a 7+3 in the left side

bobble

what about 7+4?

L-mino going down turning right

Deusovi

not possible if you push snake left like that

bobble

what about this?

Deusovi

talking about the left side

not the bottom

bobble

7:09 PM

ah, yeah, left side has contradiction. you are right

so R6C7 & R5C7 are non-snake

Deusovi

bobble

wait how did those new snake segments show up?

Deusovi

B has to use one of the two cells to their right

to be a nonrectangle of size 7 or 8

bobble

ah makes sense

it's weird that we've spend so much time on this and still haven't put down a single number

just spots that there must be numbers of some sort

and I think now we can return to my earlier rabbit hole - if R5C9 is a non-snake, then it and B can't both be non-rect

Deusovi

yeah, guess that's what happens when the snake is such a big part of it

bobble

7:15 PM

so therefore it is a snake

Deusovi

agreed

bobble

now, I think B can't be an 8 because we can't fit another 8 below it and snake can't cover the bottom

or can we?

yep think we can

drat

here's something (?) if the snake ends at C then B is an 8

and it can't end at R9C9, or a rectangle appears

wild rectangle appears

Deusovi

does it?

bobble

R9C9, not R9C10

Deusovi

ahh

whoops

agreed

bobble

7:30 PM

however, R6C9 cannot be snake - if it is snake, then B would have to be 9 to prevent a rectangle

oh woops nope

oh wait yep, because it must be 9 to prevent it or below part for Rectangl-ing

and it can't be 9, so R6C9 is nonsnake

Deusovi

oh yeah actually

if R8C8 is snake, then we either block off C or screw up the right side

and so the snake ends at the dot above C

ooh and it has to go in the staircase pattern because otherwise it blocks off a thing

bobble

why can't it go through R8C8?

Deusovi

breaks the 1 clue in C10

bobble

oh yep

Deusovi

bobble

7:36 PM

WE HAVE NUMBERS NOW

Deusovi

YEAH

ok i think e can't be snake now

because we can't fit an 8 in to the area above it, or R8C3 becomes a rectangle

bobble

do you mean it has to be snake?

no

ah yep I see

7:39 PM

so D is snake, which gives a bunch more snake squares

Deusovi

yep

uh

uh oh

did we break it

bobble

we can put a 3 on the bottom

no we broke it

demonstrate why?

7:41 PM

oh no!

aaaaaaaaaaaaaaaaaaaaaaaaahhhhhhhhhhhh

how far to backtrack?

Deusovi

i checked and it looks like my "must be staircase pattern" was wrong

bobble

could be - then |?

Deusovi

right

i thought it would block off R8C9

so that brings us here instead

oh and another 3 goes in that corner just above the lower 7

bobble

agreed

Deusovi

and now e can't be snake because it can't go to the right, and we can't fit a 7+3 on the left if it goes straight up

bobble

7:47 PM

yes, that makes sense

Deusovi

bobble

the snake segments on the top can go one of two ways, and this one doesn't work

Deusovi

ah yep

bobble

we can place a 5 now

the L below the A's 7

Deusovi

ah yep

and the 7 region at the bottom left must extend upwards on its left side, not the right (because then R6C5 would be trapped)

which places another 5

bobble

7:51 PM

that finishes the snake off, right?

Deusovi

yep, and now there's only one way to dissect the middle area!

bobble

I can see the way, but I'm having trouble justifying it to myself

Deusovi

bottom empty cell must be a 5

(nothing bigger fits, smaller things conflict with 3)

hm wait a sec

yeah ok

if it was a T it'd make a rectangle

so that 5 must be an N pentomino

bobble

11 squares left

so 5 + 3 + 3

Deusovi

nope

can't do 5+3+3

bobble

7:56 PM

oh no way to fit

Deusovi

(i thought it was that for a sec too, then i realized i'd have two 5s touching)

it has to be 8+3

bobble

but that breaks the 1s... oh wait it doesn't

wow this was a hard puzzle

Deusovi

neat conclusion

yeah it's hiding just in the middle there

hard but pretty good - i wonder if there was a less bashy way through the snake placement part

bobble

mind-bogglingly complex logic there

we did bash a lot, didn't we

Deusovi

(yeah connection issues)

that was fun though!

bobble

7:59 PM

I am giving myself 25% of the credit

Deusovi

nah you definitely did more than 25%

bobble

33%

Deusovi

i'd say more than that too

bobble

< 50%, for sure

Deusovi

but no point in figuring out exactly how much each of us did - we solved it!

bobble

8:00 PM

yay!

this chatroom will stand as a record of That Time Deusovi and Bobble Solved That Crazy Fillomino

Deusovi

hooray!

bobble

I have to leave to do life stuff now

Deusovi

alright, see ya! i should probably do other stuff too

Transcript for

[grid-deduction] Puzzle Solving