Logic Masters Deutschland e.V.

To Christmas 2021 some eager puzzlefriends have again arranged a group in which everybody had to make anonymously a puzzle for someone else. These puzzles are now presented one after the other here in the portal.

The star compass

An icy wind hissed around the gnomes' ears as they were out delivering gifts. "Froglegs and fiddlesticks," cried Fips, the head gnome. "In this weather it's impossible to find the correct route." The gnomes traditionally delivered gifts at night, you see - since time immemorial, so as not to be seen - and would orient themselves to the stars. But in this weather the stars were indistinguishable. "No problem," said Schnips, the tech gnome. "For situations like this we've always got a star compass with us." This device showed them, even in foul weather, the current state of the constellations, so the gnomes could design their route by them. But today nothing sensible seemed to be emerging from the star compass. "It's like it's bewitched," cried Fips. "Why does it just spit out a few crosses and a bunch of numbers?" Schnips went red with embarrassment and stammered a little: "Well, um, recently I took a screwdriver to the device a bit, and tried out a puzzle mode on it... and unfortunately didn't set it back to its original state." With a bit more courage, he continued: "It's really not a problem, though! What you see here is indeed the star map... just encoded. Each digit is either a classical compass direction, or it gives the distance to the next star in the given direction - but it could also be both at once. The measurement is always of the distance between cell centers. The grid has been divided into several star systems, so that each compass is associated with a single system, and each system contains two stars. The stars may not touch one another, not even diagonally, and they may not lie directly on compasses. In addition, each row and column contains exactly two stars." The head gnome shuddered: "Do you mean to tell me that we need to solve the puzzle before we can even begin delivering the presents?" He took a deep breath, then spoke a bit more calmly: "What's to be done, let's just get on with it." Can you help the gnomes master their situation?