Friday, 31 July 2009

Friday Puzzles #8

So it’s perhaps a little odd to have the 8th posting up before I actually finished the 7th one. But that’s the way I roll. Today, continuing on the whole topological theme, I have applied the Toroidal “constraint” to Masyu. That is, lines are allowed to run off the left and come back on the right, and off the top and back on through the bottom. Some might say it’s simply Euclidean space quotiented out by the word ab-1b-1.

Now I say “constraint”, because actually in Masyu having an edge is quite a big thing – so some of the logical deductions you make might seem counter-intuitive.

Bonus points if you can identify the homology class of this loop – using a sensible choice of generators a and b. :)
    #012 Toroidal Masyu – rated medium
All puzzles © Tom Collyer 2009


  1. I think I’m missing something in the puzzle. Three whites in a row mean lines have to go through each individually and not the set, as otherwise you’d have to turn in one of the white cells to satisfy the middle of the three. However, a black on the edge means you need a line coming into the puzzle. So in the top left, I’ve end up with a T-shape in that line of four at the right side of row 2.

    What am I doing wrong? :(

  2. Yeah, your logic is perfect re the three adjacent whites – what’s happening in this case is the toroidal “constraint” coming into play. There is no edge so your deduction for the black isn’t valid. That’s why I say “constraint” – what it actually is happening is a constraint is being removed.

    Anyhow, the line coming out of the black has to come out through the left edge of the puzzle, and back in through the right. Actually, if you look at the black in question, it cannot go down either – as there is a another black directly below it. So it then has to go up, and hence out through the top edge and back in through the bottom.

    Hope that clarifies, thanks for giving it a go :)

  3. I’ve updated the appearance of the puzzle slightly – I’ve removed the border to try and avoid any possible suggestions that the puzzle has an “edge”.

  4. Ah yes, my bad. I really should pay more attention to the puzzle instructions. :(

    I did try to do it at lunchtime, but as I’m not quite up to the standard of some of the Nikoli regulars I didn’t have the time to finish it off. (I generally aim for anywhere from the medium time to halfway between medium and fast, depending on how much I’m paying attention!)

  5. My topology is somewhat rusty/nonexistent so my notation may be off, but I would guess “a”. (crosses across from right edge to left edge once.)


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