Tag Archives: pure loop

Puzzle 86: Scarcity

Pure Loop Loop: Draw a loop that passes all white cells and no black cell such that the loop goes horizontally or vertically at all times and never touches or crosses itself.

Expected difficulty Easy • Answer • Comment/E-mail if you want a solution to be published

Puzzle 86: Pure Loop

Puzzle 86: Scarcity
Pure Loop
(click to enlarge)

Page 12 of Chessics #12 states that a 8×8 Pure Loop puzzle only needs four black squares to assure uniqueness of the solution, and page 143 of The Games and Puzzles Journal #8-9 states that with an addition of rows and columns (and black squares), the solution can be extended. However, I don’t find anything about how many extra black squares are necessary, so here I’ll give an upper bound: a 4n \times 4n Pure Loop needs at most 2n black squares to ensure a unique solution. In fact, the result can be generalized to a rectangle: a 4n \times a Pure Loop needs at most 2n black squares to ensure a unique solution (although obviously this is weak if a is small compared to 4n). Is there anything stronger?

Puzzle 85: Loose Strands

Pure Loop Loop: Draw a loop that passes all white cells and no black cell such that the loop goes horizontally or vertically at all times and never touches or crosses itself.

Expected difficulty Hard • Answer • Comment/E-mail if you want a solution to be published

Puzzle 85: Pure Loop

Puzzle 85: Loose Strands
Pure Loop

There we go, the last of the series. Of course, the blog is turned off again for the moment, at least until I manage to construct more puzzles. I’m busy too, you know. (By the way, expect things.) Answer key would be “lengths of horizontal segments in row/vertical segments in column” for R1/C2 (or R2/C1 or something).

Another difficult “opening”. Also for some reason I find sudden interest on Pure Loop and Heteromino now, like exploring two untouched lands… (Okay, I think I see it being used in more things now, but still.) Did you know that Heteromino almost got into FAST (as an uninteresting 3×3), but Deb decided it was too obscure and got replaced with Kakuro, which in turn also got replaced by Next Term? The more you know.