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Why is this happening? Hitori

 
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Why is this happening? Hitori - 4/18/2018 7:49:17 PM   
Vitol

 

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If you see any solved Hitori, the black squares are always connected diagonally with another black square, and this with another and so on until they reach one of the sides of the puzzle. Nothing like "island black squares", but the rules don't say anything about this.
Why is this happening? What is the math behind this?
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RE: Why is this happening? Hitori - 8/23/2018 1:20:25 AM   
flarbear

 

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This has gone a long time without an answer. I'm not a puzzle creator, but I can speculate on why puzzles are constructed this way. I believe that it has to do with the rule that a mark cannot divide the grid.

The long chains create opportunities where the solver has to decide which of two cells in one row or column need to be marked and they find that one of them must be left open because filling it in would connect a pair of those long chains and divide the puzzle. If all of the cells were disconnected throughout the puzzle, then that rule wouldn't come into play in solving it. And given that this rule is one of the more abstract rules that requires a more global awareness of the entire grid in order to apply, it is thus a popular one to use to make the puzzles harder to solve.

(in reply to Vitol)
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RE: Why is this happening? Hitori - 8/24/2018 7:05:53 PM   
Ahlyis

 

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Flarbear's response doesn't seem correct to me. There cannot be any "loops" in the puzzle or the puzzle becomes unsolvable.

Picture a puzzle that you are solving and you've reached a point where you only have 2 squares left to decide whether they are black or not. These two squares, if left clear would form the loop around a group of black squares, as Vitol is asking about. In that case, you could never solve the puzzle because either one of those squares "could" be black and the other clear and the puzzle would still be "solved correctly".

Any disconnected group of black squares, not connected to any edge of the puzzle, would necessarily allow multiple solutions to the puzzle.

(in reply to flarbear)
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RE: Why is this happening? Hitori - 8/27/2018 10:03:26 PM   
Vitol

 

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what about the forced isolated '7' black square on the right bottom? This case wouldn't drive us to a multiple solution puzzle
and i never saw something like this (the example is wrong just for show u the case)

(in reply to Ahlyis)
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RE: Why is this happening? Hitori - 8/31/2018 8:01:36 PM   
Ahlyis

 

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That's an interesting example. It's hard to say whether it is valid or not since the rest of the puzzle is unsolvable. But as a concept, I cannot immediately see any reason why that shouldn't work.

Okay, I withdraw my claim that an unsecured group would necessarily mandate multiple solutions. I'm not yet convinced there isn't anything to it since we don't have a legitimate example so far, but I'm no longer certain either way. ;)

(in reply to Vitol)
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