Logic Masters Deutschland e.V.

To Christmas 2024 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.

Santa’s workshop was pretty busy this year. After seeing the preferences of this year’s recipient, each gnome was brimming with ideas:
“We have to do a Japanese Sums! We know this person loves Japanese Sums, it should definitely be some variant of it”, said the first gnome. “But they said their favorite genre is U-Bahn! And we all know Japanese Sums and U-Bahn don’t combine well, their clues get overlapped and it looks like a mess! We should stick to an U-Bahn.”, argued another.
“Come on, there have been combinations of Japanese Sums and U-Bahn before. Just look at all those Summation U-Bahns, that’s essentially the same thing.” said a third gnome. “But they already solved most of them! How are we supposed to be creative and wreak havoc on a grid if they already solved it quite a few times!” yelled the last gnome.
After seeing all the fuss, Santa let out a mild sigh and addressed them all: “Hey now, the recipient mainly said they like arithmetic deductions. That’s not limited to Japanese Sums only. Figure something out, we are already behind schedule”, and dismissed them all.
Few hours later, the gnomes came back with a parchment. “The gift is ready!”, they announced. “We made an U-Bahn hybrid that looks exactly like a Summation U-Bahn, but just to be different, we made a Multiplication U-Bahn instead.” Santa frowned, “Really? Is that even logically diverse enough? And the clue sizes can get out of control”, but while saying that, he looked at the grid more carefully. “Hmmm, this may actually work. So, you used 1’s for corners, 2’s for straights, 3’s for branches and 4’s for crosses, all instances of products are separated by at least one cell not visited by the loop network, and you guys ciphered it for good measure?”
“Yes! But sadly, our recipient’s name is too short, therefore we only ciphered the letters in their name such that each letter will correspond to exactly one digit. For all instances of the ciphered digits, the ciphered letter is used. For all other numbers, we used ?s.” “And of course we made it chaotic! For each clued row or column, we gave two different sets of products. Only one of those sets of clues is correct, and he must figure it out for all clues! The other set is always a complete gibberish, but the cipher rules apply to all clues, otherwise it would be impossible to tell which one’s are lying!”
The last gnome was grinning ear to ear while he uttered these sentences. Santa wasn’t over the moon, but he wasn’t sad either, as this chaotic group could have made something so much worse.