Friday Puzzle #135 - Loop the Loops (DD Part 8)
This weekend marks the last chance to compete in the LMI Puzzle Marathon test. It's a unique contest with 10 separate puzzles you can solve at any time, against their own clock, but with large puzzles that can take dozens of minutes to dozens of hours to solve depending on your skill. One of the puzzles is a type I explored on my Double Decathlon test, so I thought I'd repost those puzzles this week for any who might want the practice. I've discussed strategies for solving this puzzle type before too.
Rules:
Draw a single closed loop that connects neighboring dots horizontally or vertically (but not diagonally). The loop cannot intersect of overlap with itself.
Some numbers appear in the grid as clues; as in a Slitherlink puzzle, a numbered square indicates exactly how many of its four edges are used by the loop.
Some circles (either white or black) also appear in the grid as clues; as in a Masyu puzzle, the loop must pass through all of these circles. When passing through a black circle, the path must make a 90 degree turn and extend at least two dots in both directions. When passing through a white circle, the path must go straight and must turn at at least one of the adjacent dots.
Example Solution:
Easy:
Hard:
When merging two styles with different design rules (Slitherlink is always symmetric, Masyu is rarely symmetric), it is hard to know exactly what the hybrids should look like. I took two rather different approaches with the puzzles here.
The first "Easy" puzzle is fully symmetric. Moreover, when looking at clue identity, it is fully anti-symmetric. All white circles have a rotationally opposite black circle. And every 0,1,2,3 slitherlink clue has a rotationally opposite 3,2,1,0 clue. I almost got a nice diagonal pattern with the numbers but had to move one pair of givens at the end (you'll know which ones) to get the final puzzle to work just right. Still, after making this puzzle, I find the presence of different styles of clues makes the symmetry much harder to pick out than in a normal Masyu or Slitherlink alone, but perhaps this particular pattern of circles and numbers is part of the problem.
The second "Hard" puzzle throws symmetry considerations out the window, and instead takes a quadrant theme to some interesting places. Each quadrant has only one kind of Slitherlink clue, and even numbers share space with white circles and odd numbers with black circles. I chose this arrangement as a lot of the interesting effects of black circles in a slitherlink hybrid are with odd numbers, where the white circle effects are more subtle but definitely lead to a challenging lower-left corner. This puzzle also uses some "loop" constraints, such as free end counting, near the finish, which made the puzzle the right difficulty for the test. I hope you enjoy both of these, and agree with me that more Loop the Loops would be nice to see.
Solutions:
Easy
Hard
Rules:
Draw a single closed loop that connects neighboring dots horizontally or vertically (but not diagonally). The loop cannot intersect of overlap with itself.
Some numbers appear in the grid as clues; as in a Slitherlink puzzle, a numbered square indicates exactly how many of its four edges are used by the loop.
Some circles (either white or black) also appear in the grid as clues; as in a Masyu puzzle, the loop must pass through all of these circles. When passing through a black circle, the path must make a 90 degree turn and extend at least two dots in both directions. When passing through a white circle, the path must go straight and must turn at at least one of the adjacent dots.
Example Solution:
Easy:
Hard:
When merging two styles with different design rules (Slitherlink is always symmetric, Masyu is rarely symmetric), it is hard to know exactly what the hybrids should look like. I took two rather different approaches with the puzzles here.
The first "Easy" puzzle is fully symmetric. Moreover, when looking at clue identity, it is fully anti-symmetric. All white circles have a rotationally opposite black circle. And every 0,1,2,3 slitherlink clue has a rotationally opposite 3,2,1,0 clue. I almost got a nice diagonal pattern with the numbers but had to move one pair of givens at the end (you'll know which ones) to get the final puzzle to work just right. Still, after making this puzzle, I find the presence of different styles of clues makes the symmetry much harder to pick out than in a normal Masyu or Slitherlink alone, but perhaps this particular pattern of circles and numbers is part of the problem.
The second "Hard" puzzle throws symmetry considerations out the window, and instead takes a quadrant theme to some interesting places. Each quadrant has only one kind of Slitherlink clue, and even numbers share space with white circles and odd numbers with black circles. I chose this arrangement as a lot of the interesting effects of black circles in a slitherlink hybrid are with odd numbers, where the white circle effects are more subtle but definitely lead to a challenging lower-left corner. This puzzle also uses some "loop" constraints, such as free end counting, near the finish, which made the puzzle the right difficulty for the test. I hope you enjoy both of these, and agree with me that more Loop the Loops would be nice to see.
Solutions:
Easy
Hard
