Remembered Length Description

Remembered Length is a puzzle original to this blog to the best of my knowledge. The object is to draw an oriented closed loop — oriented meaning it has a defined forward and backward direction — passing through every grid square exactly once through adjacent squares. The grid has some rooms given, and some have given numbers. Rooms may be visited any amount of times. Each time the loop exits a room with a number N, it must pass through exactly N squares in the next room it visits before exiting. Rooms without given numbers have no such restriction; the lengths of the paths in the next visited rooms may all be the same or may all be different.

Below is an example puzzle and its only solution. The orientation of the loop, which is unmarked in the image, is that it is going right at the top-left corner.

Example problem Example solution

Additional features:

  • Black squares are not part of the grid or any room, and should not be passed through in the loop.
  • Some regions may be shaded or colored. Unless otherwise noted in the rules to a variation, this is for aesthetic purposes only and has no bearing on solving.
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