Sudoku Islands

I have just managed to complete both of these puzzles from the Community section of issue 10 and absolutely loved them! (and Tom if you read this then I would have commented on your own site but not being a mathematician was unable to answer the anti-spam question - hangs head in shame!!)

For some reason I've always had a bit of a block with nurikabe puzzles except for the very easy ones, but the idea of combining it with sudoku really appealed and I decided to give it a go. I actually found the 12 x 12 easier than the 9 x 9. The addition of the sudoku numbers limited the course which the islands could take and I found myself shading in bits of islands and then putting a dot in any squares where there would have to be a number. As soon as I had 5 shaded squares in any row or column (in the 12 x 12 grid) then I put dots in the other 7, which in turn gave more clues for the islands. At the end I had all the islands in place, and then was able to fill in the sudoku bit. Took me quite some time to reach this point, but had a great sense of satisfaction at the end! Would love to have a go at some more sometime please!

Is that the 3-4-5 triangle question? If so it's 5. And I agree - these are incredibly good puzzles from Tom.

If you want a further challenge, you can solve the islands part of the 12x12 one without using the sudoku clues - just the given island clues and 5-per-region constraints are sufficient! That itself is a truly spectacular puzzle.



Edited 2 time(s). Last edit at 09/18/2010 11:08AM by gareth.

That's the question. Since it's (cough) 30+ years since I took my maths O'level as they used to be called, I'd forgotten what the hypotenuse was!. Dare say I could soon remind myself if I had a mind, but would rather spend the time puzzling! The way you describe above is more or less the way I solved it. It really helped knowing there was a limit to the number of shaded squares per region as in normal nurikabe I often get lost and end up giving in. It's always a good feeling when you get to grips with a new puzzle type.

I've only just come across these forums - so my apologies for the delay in the reply. With regards to my anti-spam question - it asn't my intention to exclude interested parties - I simply wanted a very wordy question with a one character answer to put off any potential spambots which target the Warwick blogs, without inconveniencing any human commentators!

Firstly I'm delighted you've enjoyed my puzzles - its exactly the sort of feedback any puzzle author wants to hear! I'm afraid I haven't had much opportunity to develop the initial idea further, and as such I actually think I've only really dipped my toes into the potential of this. It's my opinion at the moment that the idea is still something of an uncut diamond at the moment.

As someone who commented on the blog ages ago said, it's possible to do all the puzzles I've done so far by solving the islands element of the puzzle without having to think about any sort of sudoku solving. If the idea is going to continue in its current form then I'd like to see some proper hybrid logic - i.e. having to have to do a bit of sudoku in order to progress with solving the islands. The trouble is, because the given number clues are implictly island clues too, the island element of the puzzle is very constrained. So as Gareth hints at, one evolutionary path is to drop most of the sudoku part of the puzzle, and simply require that you have a set islands/sea ratio for each row, column and box.

The next issue is that I've confused a lot of long-time puzzlers with the whole reversal of the Nurikabe colour scheme. The trouble is, it's more convenient to have the sudoku part happen in the sea part of the puzzle rather than the islands, but obviously it's a mess if you then have to write numbers into squares you've already shaded in. The idea that comes to mind is to reverse that reversal, and have numbers in the islands instead and the sea being shaded in. I'd probably have to drop the 3x3 box constraint here, but perhaps you could have islands all of the same size, with no digits repeated - or perhaps sudoku clues could double up as clues to the size of islands - so if you saw a 5 you'd know you'd have to find an island of size 5, and then fill in the 4 remaining squares with 1-4.

These are all ideas I'd really like to play around with. Unfortunately of late I've had to juggle a lot of the process of administering the upcoming UKPA sudoku championship, and then the (rather disastrously) rushed LMI puzzle test. Long term projects will involve a couple more LMI tests (at a more leisurely pace!) - but you can be sure that these ideas will be developed sometime soon!

Tom

Will look forward to seeing what you come up with in due course! Just remember to include a couple of not so difficult ones in there whilst we get to grips with them! I used to only ever do sudoku and its variants but am trying to branch out a bit more these days,