It's almost amazing that one can solve this with so few numbers revealed to begin with. Great puzzle, Gareth!

Posted 3rd Jun 2024 at 12:30

gareth Administrator Daily subscriber Has started but not yet finished this puzzle

Yes, it's an interesting point. It's well-known that the minimum givens for a regular sudoku is 17, but I wonder what it is for a wraparound (or jigsaw) puzzle. This one has 14, so clearly it has to be 14 or fewer (and 8 or higher, obviously).

Posted 3rd Jun 2024 at 12:32

gareth Administrator Daily subscriber Has started but not yet finished this puzzle

I also think that this is a good way of objectively explaining why this type of puzzle is harder than a regular sudoku. It makes clear that each square has more impact than in a regular puzzle, making it harder to see the full implication of each placed digit or set of possible digits. Add to that the fact that it's much more tricky for a human to scan irregular shapes (especially wraparound ones) and I think that it's easy to see why these can be so hard.

Heh. It's funny you say that it's obvious that you need at least 8 numbers... but it's not so obvious to me! I cannot even begin to figure out how someone might calculate the minimum givens for a puzzle! Fascinating stuff.

The minimum of 17 clues for a standard sudoku was proven by exhaustive search for 16-clue puzzles (https://arxiv.org/abs/1201.0749).

The number of minimum clues for a sudoku depends on the shapes of the regions: a regular sudoku is also a kind of jigsaw sudoku (we had this before with 3x2 fields! :-) ). So you can't specify the minimum number of clues for "a jigsaw sudoku", you'd have to specify the region shapes as well.

For certain shapes, you can get down to 8 clues (http://www.bumblebeagle.org/dusumoh/9x9/index.html). ("obvious", though, ...? ;-) )

Posted 9th Jun 2024 at 18:27 Last edited by gareth 9th Jun 2024 at 18:32

gareth Administrator Daily subscriber Has started but not yet finished this puzzle

It's 'obvious' that 8 is a bound on the minimum because for any puzzle where the symbols are independent (i.e. there are nine independent symbols to place with no relationships between them other than elimination via prior placement in a region) then you need to have 8 different symbols already placed in order to have a unique solution. Otherwise, with 7 or fewer symbols, you would always be able to swap all of the 8th symbol with all of the 9th symbol, giving two different (even if just trivially so) solutions.

Of course, 8 being a bound is not at all the same as it being obvious that 8 is actually possible - so that link is very informative! Thanks for sharing.

For puzzles with relationship constraints, such as inequalities or consecutive and so on, this is obviously not true.

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Add new comment)ModerateCompletion time:14:12ModerateCompletion time:14:12EasyCompletion time:10:53The number of minimum clues for a sudoku depends on the shapes of the regions: a regular sudoku is also a kind of jigsaw sudoku (we had this before with 3x2 fields! :-) ). So you can't specify the minimum number of clues for "a jigsaw sudoku", you'd have to specify the region shapes as well.

For certain shapes, you can get down to 8 clues (http://www.bumblebeagle.org/dusumoh/9x9/index.html).

("obvious", though, ...? ;-) )

Last edited by gareth 9th Jun 2024 at 18:32boundon the minimum because for any puzzle where the symbols are independent (i.e. there are nine independent symbols to place with no relationships between them other than elimination via prior placement in a region) then you need to have 8 different symbols already placed in order to have a unique solution. Otherwise, with 7 or fewer symbols, you would always be able to swap all of the 8th symbol with all of the 9th symbol, giving two different (even if just trivially so) solutions.Of course, 8 being a bound is not at all the same as it being obvious that 8 is actually possible - so that link is very informative! Thanks for sharing.

For puzzles with relationship constraints, such as inequalities or consecutive and so on, this is obviously not true.

EasyCompletion time:10:53Add new commentAdd a commentYour comment:You can however view other players' statistics and comments in the tables above.

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