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.

„I welcome all puzzle types, just please no...“, the head gnome read from the wish list during the puzzle assignment session. At that moment - late as usual - the new Sudoku gnome apprentice burst into the room and only heard "...Sudokus."
"Hooray, hooray!" the apprentice shouted and leapt for joy. "Finally someone is asking for a Sudoku!" He was completely beside himself and out of control. "NO Sudokus. The giftee is asking to have NO Sudoku!" "What?! - but I was so looking forward to it, and now I don't get to prepare any puzzles at all for the gift exchange..." The little gnome curled up into himself, looking terribly dismayed. The head gnome felt bad for the little guy and came up with a plan: "Why don't you go help the other gnomes with their puzzles". And soon the gnome assembly was once again buzzing with activity.

After a few days the Double-Block-gnomes came to the head gnome to complain: "We can't do this anymore! The new Sudoku apprentice isn't allowing us to create a Double Block (1-4). In a puzzle no two identical cells can be in the same row or column, to say nothing of black cells." They had hardly even left the room before the Skyscraper gnomes stood in his office: "Now we had nearly completed our Skyscraper Puzzle (1-6). Then this Sudoku fiend came in and erased all of our hints! A riddle has no clues on the outside."

The head gnome decided to make the rounds. But the gnomes responsible for the Domino Searches* were not in their workshop. He found them in the back office of the skyscraper gnomes. That's where they had decided to hide from the eager young Sudoku apprentice. When he stepped back into the corridor he was nearly run over by the chief gnome of the Japanese Sums** team. "I need to get out of here!" cried that one, as he fled. The head gnome stepped into the Japanese Sums workshop. "Nee how!" came the greeting of the sudoku apprentice. The others rolled their eyes. "Because we're making a Japanese Sums puzzle, the guy learned a couple of phrases in Chinese. And each time we want to carefully check our arithmetic, he breaks our concentration with his repeated 'Nee how!' Finally the chief shouted at him: 'Nee HOW!? Well, HOW would you like me to box you about the ears!?' And with that he had run out, because he didn't want to be put in puzzle jail for committing assault."

The head gnome was tearing out his hair by now. "How am I to solve this one now? If my gnomes can't get their work done properly and are even starting to fall over each other..." The great grand-gnome, who had been observing the scene, took the head gnome aside for a word or two. Finally, the head gnome said "Yes, that is how we will do it. What a wise decision." He turned to the insulted Sudoku gnome and declared: "All right, young one. You may create a Sudoku: a 4x4 Diagonal Sudoku ." As he departed, he could be heard to mutter: "As long as the puzzle is ready for a punctual delivery!"

Figure out which puzzle type occurs how often, and with which diagram(s) it is associated. The grey-tinted cells indicate where the diagrams overlap. If a blackened cell overlaps a puzzle type without blackened cells, then the blackened cells in the latter puzzle are equal to 5 or 6. In the whole puzzle there are exactly three such cells. Solve the puzzle and then assemble the individual diagrams into a single picture - use only the diagrams, omitting any outside clues.

* = Domino Search: dominos from 1-2 up to 5-6 (no pairs such as "1-1") once each, and 6 blackened cells
** = Incomplete Japanese Sums 1-6; each dot stands for a digit; two-digit numbers cannot begin with zero.