This is a Friday special puzzle. Because of the P.I.HUNT, I am two puzzles offset for Fridays to be multiples of 5. Luckily, 50n-1 and 50n are traditionally special type puzzles, started from MellowMelon I believe.

49 is a square number, and so are 4 and 9, what a good time for a milemarker square made of square themed squares puzzle.

RULES:

Draw a loop passing through centers of cells, traveling parallel to the edges, going through each cell at most once

Top left: Shade in every cell the loop does not go through. Unshaded numbers truthfully represent how many of their 8 orthogonal neighbors are shaded in this region, whereas shaded numbers lie, and give a number other than how many of their neighbors in this region are shaded.

Top right: There are some multicelled regions in this section, which are repeated. Within each copy of the same shape, the loop must be exactly identical. The loop doesn’t necessarily pass through every region.

Bottom Left: Masyu puzzle, however, the white circles are optional, the loop doesn’t have to pass through them, and the black circles are full, every possible black circle is given

Bottom Right: Rightface puzzle, with multiple robots entering at every spot that the loop enters this region going clockwise around the loop. Each robot travels at the same time, and follows the rightface rules and must exit the region following the loop. It is a condition on the solver to prevent two robots from wanting to enter the same square at the same time. Some black cells are already given.

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I have several questions on the rules here. One is how I know that any of the loop exists, but I’ll let that slide.

1. In the upper left, does a number count all the shaded cells in a 3×3 area, or just in the eight cells forming a ring?

2. In the upper left, does a number count any untraveled cells outside the quadrant as shaded?

3. In the lower right, if a robot has to consider whether to cross an internal edge of the quadrant (e.g., it takes one step forward and a second step would take it across), does it always cross the border? Or does it depend on whether the square on the other side was recently occupied?

Depending on the answers, it seems the answer might be very trivial. (If this particular answer is right, the huge puzzle is way overdesigned.)

You know there is a loop or else r10c10 would be incorrect.

1. Just the eight cells forming a ring.

2. “orthogonal neighbors in this region”, so ones outside the region don’t count

3. It always does

Based on your last comment, I think you already know the answer. See Evil Zinger puzzles on Grant Fikes’ blog or puzzles 99, 149 etc. on Mellow Melon’s blog. 🙂