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 Long Journey

The gnome Markus was intensely agitated. He had been permitted to take part in the first-ever intergalactic Christmas exchange program, and tomorrow the great journey was to commence. He was going to Alpha Centauri and looked forward to the surely interesting new experiences. He headed over to the (also newly inaugurated) travel bureau at the Department of Gnome Affairs to pick up the newest set of instructions.

The agent in charge pushed a map across the table toward him, cleared his throat, and began to explain: "Now, Markus, as you surely are aware, the Centaurian people are mathematically obsessed with Minmax reasoning. They sent us a map with cryptified clues, which is to be interpreted as follows: It is an 'ordinary' Japanese Sums puzzle, but — Alpha Centauri being a sphere — with blocks that can continue at the other end of the row or column. The clues are cryptified in the regular manner, with each letter belonging to exactly one digit, and vice versa. Note, however, that wherever equal sums appear in a row or column, only these equal values are cryptified, and all the other sums were represented by greater-than and less-than symbols. These are notated in terms of the cryptified value that shares that row or column. If no equal sums appear, then — see the clues in parentheses — only the maximum and minimum sums were given. Be careful here, though, for it can definitely happen in such rows/columns that more than two blocks of digits can appear. The marked blue dots indicate wherever consecutive digits appear in neighboring cells. All such blue dots are given. There are three more things you must know: the blackened fields that separate the sums are never in orthogonally neighboring cells (a restriction that also applies across the outer edges), and further the first shown clue always refers to the leftmost or topmost block. (Note that this does not apply to the clues in brackets, where instead you see the minimum printed in front and the maximum in back.) And lastly, you are surely already aware that the Centaurians use a base 12 system, and all digits from one to eleven can show up in the grid, and can be (along with zero) cryptified. So that about does it! Have a pleasant journey!"

Markus nodded. He had already expected that the job was going to be a tough nut to crack. But the journey was long, and he was optimistic about completing the map before his arrival.