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Every 5x5 Nonogram

pixelogic.app

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Re: Every 5x5 Nonogram

#62

Earlier quoted context omitted.

I don't know exactly how okayestjoel's solver works, but here's an example of a nonogram which I imagine it would consider "difficult": 1 1 1 2 1 1 2 1 2 . . . . . 2 . . . . . 11 . . . . . 2 . . . . . 11 . . . . . This puzzle has a unique solution (141a706), but none of the clues immediately tell you anything about the state of any specific cell.

Thanks, it's a nasty example. [spoiler alert] Naming the coumns ABCDE from left to right, and the rows 12345 from top to bottom. Let's consider B2 near the top left. If B2 full: Then B1 is empty because B has "only" ones. Then the "two" block in row 1 must make D1 full. Then D2 is also full because D has a "two". Now B2 and D2 are full, but that's impossible because B has only a "two". So the B2 must be empty. From t…

If you assume that a cell is full and then get a contradiction, this is pretty much a backtracking to a computer. So it is reasonable that the solver does not do this trick.

Re: Every 5x5 Nonogram

#63
Some fun boards:

The empty board: https://pixelogic.app/every-5x5-nonogram#21035201

The full board: https://pixelogic.app/every-5x5-nonogram#13821100

A greeting board: https://pixelogic.app/every-5x5-nonogram#4282670

A checkerboard: https://pixelogic.app/every-5x5-nonogram#24204839

A board of love: https://pixelogic.app/every-5x5-nonogram#14090887

Question block: https://pixelogic.app/every-5x5-nonogram#18519948

Re: Every 5x5 Nonogram

#64

Earlier quoted context omitted.

I don't know exactly how okayestjoel's solver works, but here's an example of a nonogram which I imagine it would consider "difficult": 1 1 1 2 1 1 2 1 2 . . . . . 2 . . . . . 11 . . . . . 2 . . . . . 11 . . . . . This puzzle has a unique solution (141a706), but none of the clues immediately tell you anything about the state of any specific cell.

Thanks, it's a nasty example. [spoiler alert] Naming the coumns ABCDE from left to right, and the rows 12345 from top to bottom. Let's consider B2 near the top left. If B2 full: Then B1 is empty because B has "only" ones. Then the "two" block in row 1 must make D1 full. Then D2 is also full because D has a "two". Now B2 and D2 are full, but that's impossible because B has only a "two". So the B2 must be empty. From t…

Now I wonder if there are any 5x5 nonograms which can be proven to require multiple levels of backtracking, i.e. where you have to make at least two guesses before reaching a contradiction, no matter where you put those guesses.

Re: Every 5x5 Nonogram

#65
post #62

Earlier quoted context omitted.

Thanks, it's a nasty example. [spoiler alert] Naming the coumns ABCDE from left to right, and the rows 12345 from top to bottom. Let's consider B2 near the top left. If B2 full: Then B1 is empty because B has "only" ones. Then the "two" block in row 1 must make D1 full. Then D2 is also full because D has a "two". Now B2 and D2 are full, but that's impossible because B has only a "two". So the B2 must be empty. From t…

If you assume that a cell is full and then get a contradiction, this is pretty much a backtracking to a computer. So it is reasonable that the solver does not do this trick.

I agree they are the same. It's just that if the try is short enough, I consider it a valid trick.

Re: Every 5x5 Nonogram

#66
post #63

Some fun boards: The empty board: https://pixelogic.app/every-5x5-nonogram#21035201 The full board: https://pixelogic.app/every-5x5-nonogram#13821100 A greeting board: https://pixelogic.app/every-5x5-nonogram#4282670 A checkerboard: https://pixelogic.app/every-5x5-nonogram#24204839 A board of love: https://pixelogic.app/every-5x5-nonogram#14090887 Question block: https://pixelogic.app/every-5x5-nonogram#18519948

How did you come to build this collection? They're all in different sections...

Re: Every 5x5 Nonogram

#67

This is my game! I was recently curious about how many 5x5 nonograms can be solved purely with logic, no guessing. After running my nonogram solver on all 33,554,432 possible pixel combinations in a 5x5 grid, it turns out the answer is 24,976,511. Inspired by One Million Checkboxes, I thought it would be cool to create a realtime, collaborative nonogram game where we can collectively try to complete all ~25 million o…

I want to be able to click-and-drag. For example, in this row

    1 2 |x x  |
if I left click the second cell and drag right it should mark all the blank cells black.

Similarly in the inverted case, if I have marked cells and right-click-and-drag next to them it should mark the empty spots I cross over with Xs.

Important: this doesn't change the state of any cell that wasn't blank to start out. You should have to click on a marked cell to clear it (or right click to replace it with an X). And similarly to above, if you drag, it should change only the cells you touch that match the starting state of your original cell to the new state.

Re: Every 5x5 Nonogram

#69
post #66
post #63

Some fun boards: The empty board: https://pixelogic.app/every-5x5-nonogram#21035201 The full board: https://pixelogic.app/every-5x5-nonogram#13821100 A greeting board: https://pixelogic.app/every-5x5-nonogram#4282670 A checkerboard: https://pixelogic.app/every-5x5-nonogram#24204839 A board of love: https://pixelogic.app/every-5x5-nonogram#14090887 Question block: https://pixelogic.app/every-5x5-nonogram#18519948

How did you come to build this collection? They're all in different sections...

I don't want to ruin the game for the community so will hold off on saying too much. I will say this- this game is very well designed so it's pretty straightforward to understand how it works without using anything more than the network tab of chrome :). No js, frontend puppeteering, etc. are needed. I might write it up when the game is close to completion!

Re: Every 5x5 Nonogram

#70

Earlier quoted context omitted.

The number of unique 5x5 grids is 33,554,432 (2^25) and the number if you ignore rotation or reflection is 4,211,744. What is 28,781,820?

That's the number of unique combinations of clues for all 2^25 puzzles. There are 13 possible clues for each row/column (0 1 2 3 4 5 11 12 13 21 22 31 111), but not all 13^10 possible combinations can appear together - for instance, 5 5 5 5 5 / 0 0 0 0 0 is obviously impossible. (I wrote a program to calculate this by generating all 2^25 puzzles and their clues, then sorting by the clues. I also verified the count of…

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