The Doppit Almanac · No. 45

Orbit

Cut the grid into pieces that turn about their dots

What it is

Orbit is Spiral Galaxies, the puzzle also sold as Tentai Show. The grid is scattered with dots, and the job is to cut the whole thing into pieces, one dot each, so that turning a piece half a turn about its own dot leaves it covering the same cells.

The dots are the whole character of it. One sits in the middle of a cell, the next on the line between two cells, the next on the corner where four meet, and each of those puts its piece on a different footing. A piece can be a single square or a fat blot of a dozen cells, and until the board fills up you cannot always tell which.

How it plays

• Every cell ends up in exactly one piece, and every piece holds exactly one dot.
• For every cell in a piece, the cell opposite it across that piece's dot is in the piece too. The cells the dot sits on are given at the start.
• A piece is one connected block. Tap a dot to pick its piece, then tap cells to add them; the cell opposite comes in on its own.
• There is always a forced next cell, and Hint finds it and says why. Nothing here needs a guess.

The difficulties

Four grids, four grains. Easy is a six-by-six with seven dots, half a minute to a minute of reading the picture. Medium is a nine-by-nine with fourteen, one to three minutes, where pieces start getting walled in before they reach the cells they want. Hard is a ten-by-ten with eighteen, three to six minutes, and every hard board holds at least one cell that only gives way to an assumption followed out until it breaks. Expert is that same ten-by-ten, and one assumption is not enough on it. At least twice a cell has two pieces that could still reach it, and the wrong one only breaks a rule after a second assumption inside the first. Expert never comes round as a daily; it is yours to practise on. A fresh board is cut every day, for nothing.

Nearby in the almanac: Groveit, Fourit and Packit