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Every 5x5 Nonogram

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Re: Every 5x5 Nonogram

#21

Post by vintermann »

stagger87 wrote: post #20
curtisf wrote: post #17

Earlier quoted context omitted.

What do you mean by "purely with logic, no guessing"? "Guess and backtrack" is a totally valid form of deduction for pen-and-paper puzzles, it's just not very satisfying. But often (always?) there is a satisfying deduction technique that could have replaced the guess-and-check, it may just be fairly obtuse. Or do you just mean where the clues for the raster don't result in a unique solution?

Not OP, but you don't ever have to guess and backtrack, you can always work out the next move. After playing about 100 boards several simple "rules" emerge which allow for this.

Yes, 5x5 is small enough that all backtracking can be codified into easily human-accessible rules.

* 5, 0, 1 1 1, 2 2, 3 1 and 3 1 are immediately solved

* 4 lets you set 3 squares immediately

* 3, 2 1 and 1 2 let you set 1 square immediately

Re: Every 5x5 Nonogram

#22

Post by gschizas »

okayestjoel wrote: post #2

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…

Why do some puzzles have a green or red border? What does this signify?

EDIT: or purple border.

Re: Every 5x5 Nonogram

#23

Post by shivbhatia »

okayestjoel wrote: post #2

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…

This is really cool!

Re: Every 5x5 Nonogram

#24

Post by [deleted] »

curtisf wrote: post #17
okayestjoel wrote: post #2

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…

What do you mean by "purely with logic, no guessing"? "Guess and backtrack" is a totally valid form of deduction for pen-and-paper puzzles, it's just not very satisfying. But often (always?) there is a satisfying deduction technique that could have replaced the guess-and-check, it may just be fairly obtuse. Or do you just mean where the clues for the raster don't result in a unique solution?

[deleted]

Re: Every 5x5 Nonogram

#25

Post by MaysonL »

scythe wrote: post #13

This is a downright hazard. I scrolled down to find one that wasn't solved yet, and the next thing I knew it was 30 minutes later and I had solved a hundred of them.

I went through 102 before i knew it.

Re: Every 5x5 Nonogram

#27

Post by questerzen »

okayestjoel wrote: post #2

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 calculated that 25,309,575 games have a unique solution. My back-tracking solver correctly finds all answers for all of the 28,781,820 possible distinct games.

Re: Every 5x5 Nonogram

#28

Post by jhanschoo »

stagger87 wrote: post #20
curtisf wrote: post #17

Earlier quoted context omitted.

What do you mean by "purely with logic, no guessing"? "Guess and backtrack" is a totally valid form of deduction for pen-and-paper puzzles, it's just not very satisfying. But often (always?) there is a satisfying deduction technique that could have replaced the guess-and-check, it may just be fairly obtuse. Or do you just mean where the clues for the raster don't result in a unique solution?

Not OP, but you don't ever have to guess and backtrack, you can always work out the next move. After playing about 100 boards several simple "rules" emerge which allow for this.

Hot take: Some valid rules are just brute-force search in an altered state space.

For example, a valid "advanced" rule is this: consider a line, then consider all permutations of ways to complete it given the current state of the line. If a square is filled in/crossed out in all these permutations, then it you may fill it in/cross it out.

This is an O(n!) algorithm! In practice you only have <5 permutations.

Re: Every 5x5 Nonogram

#30

Post by jobigoud »

vintermann wrote: post #21
stagger87 wrote: post #20

Earlier quoted context omitted.

Not OP, but you don't ever have to guess and backtrack, you can always work out the next move. After playing about 100 boards several simple "rules" emerge which allow for this.

Yes, 5x5 is small enough that all backtracking can be codified into easily human-accessible rules. * 5, 0, 1 1 1, 2 2, 3 1 and 3 1 are immediately solved * 4 lets you set 3 squares immediately * 3, 2 1 and 1 2 let you set 1 square immediately

In summary the only ones that don't let you put a square immediately are "0", "1", "2" and "1, 1". And as soon as you put a square you can put some crosses (right click). In the end it becomes fairly mechanic.
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