Puzzles I won't publish

Let's start with the only puzzle that I think may have enough merit for a place on Logic Masters Deutschland, before I move on to the juicy unpublishable bits. It's this one:

007 - Anti-diagonal killer sudoku

• Normal 9x9 sudoku rules apply: Place the digits 1 to 9 exactly once in each row, column, and region indicated by thick borders in the grid.
• Anti-diagonal: Both indicated main diagonals contain only 3 distinct digits.
• Killer cages: An area surrounded by a dashed line is a 'killer cage'. Digits in a cage cannot repeat and sum to the number in the upper left corner.

You can play puzzle 007 online in the CTC app.

Warning: there are small spoilers for 007 in the text below, where I talk about what logic I used.

This story starts with a brilliant puzzle pack by Sam Cappleman-Lynes which contains 27 linked sudokus, where none of the puzzles can be solved without the others. It is published in the puzzle archive of the CTC Fan discord server, entry 1649. I remember live streaming my marathon solve of this puzzle pack, and how it taught me about all these different sudoku variant rules I hadn't seen before.

One of them was anti-diagonal, which then struck me as a weird constraint to work with. And that is sometimes all the temptation I need to start experimenting with it.

The most constrained digit in anti-diagonal is the one in the center cell, which can only appear in 3 different places in the corner regions. So my initial idea was to draw two arrows on the main diagonals, as in below puzzle:

Anti-diagonal arrow sudoku, diagonals not drawn

Because the bottom two corner cells contain the arrow circles, they both must be larger or equal to the digit in the central square. But the corner cells see each other, and so one of them must be larger than the digit in the central square, which is therefore not a 9. Building a break-in around this idea was easy enough, but then I added the two arrows in row 2, to put more pressure to the values in the bottom corner cells, and the puzzle started to behave very strangely.

Possible locations of the center cell in red

In the diagram above, all white cells see the central square. I did not anticipate that the very fact that the central digit has to appear on one of those row 2 arrows had some complicated and interesting side-effects. I only discovered this gradually while test-solving.

I was tempted by these deductions so much that I only added some extra givens to steer the puzzle into the most enjoyable solve path I could find, and then gave it to testers. Who then told me that even though they thought the puzzle was of high quality, it wouldn't be to everyone's taste.

My immediate but hasty conclusion was that the idea only needed better telegraphing, and I started working on an anti-diagonal with killer cages, which became 007. And indeed, testers for that puzzle did find the logic, without being overwhelmed by it. Encouraged by this, I challenged myself to set a non-hybrid anti-diagonal sudoku, where I pushed the anti-diagonal logic to its limits:

Bent Triple, anti-diagonal sudoku

(N.B.: If you do want to try this out, I recommend solving 007 first. But, ... [insert several disclaimers].)

In this puzzle it's not just the central square that's restricted, but there's even logic in there that removes essential options from one of the diagonals because they see a tuple spread out over row 1.

Now, I may think that this is extremely interesting - I still do. But I don't think I should have forgotten how it took me several test solves to figure out this unintuitive behavior of anti-diagonal sudokus. So I should never have expected solvers to find all this going in blank and ignorant. If anything, the puzzle should collapse after the break-in, and it doesn't. So I hereby offer my apologies to anyone who's bashed their head against Bent Triple.

I believe now that both the arrow and Bent Triple belong to the realm of experimental studies, not to be given to solvers without any prior information.

Lastly, I apologize for breaking the promise I gave you with that title. My only excuse is that I find it hard to talk about puzzles without implicitly publishing them. At least I'm aware of the paradox, and I hope the story makes up for it.

All puzzles published on this blog are licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.