Topology on Shai Asher

The Cleaning Robot Puzzle: A Floor with a Twist

Fri, 25 Sep 2026 08:30:00 +0300

Give the cleaning robot’s floor a half twist, like a Möbius strip, and after one lap round the room its up is the map’s down, and the commands that cleaned every flat room walk it into the walls.

This is Part 5 of the cleaning robot puzzle. Part 4 glued the room’s edges into a torus, and the robot lost its ability to name fields by counting moves. This part glues two edges with a twist, and the robot loses something it never knew it had: a compass. On every floor so far, ^ meant the same direction everywhere. Here it doesn’t.

The Cleaning Robot Puzzle: A Room That Wraps Around

Fri, 25 Sep 2026 08:00:00 +0300

Glue the cleaning robot’s room into a doughnut, so that walking off the right edge brings it back on the left, and the blind robot from Part 3 never stops cleaning.

This is Part 4 of the cleaning robot puzzle, and the first of four parts in which the floor stops being flat. Part 1 cleaned a room with a depth-first walk, Part 2 added dirt, a bag and a battery, and Part 3 asked for the fewest commands, took the map away, added a dock and a second robot. Every one of those rooms was a flat grid with a wall round it.