Logic Masters Deutschland e.V.

Cyclic Generators

(Published on 9. August 2022, 22:17 by SirSchmoopy)

Links:

CTC (with solution)
F-puzzles
Walkthrough (spoilers)

Standard Rules:

Normal sudoku rules apply.

Normal thermometer rules apply. Digits along a thermometer increase starting from the bulb end.

Definitions:

Let a 'cycle' be the loop in a single row in a grid created by repeatedly going from a digit to the column indexed by that digit in the same row. For instance, if a cell contained the digit 2, the next cell in the cycle would be the cell in column 2 for that row. Then, if column 2 had a 4 as its digit, the next cell in the cycle would be the cell in column 4 and so on.

Let the 'order' of a cycle be the number of unique cells in a cycle. For instance, if column 7 contained a 3, and column 3 contained a 7, this would create an order 2 cycle.

Cycle rules:

Along with normal thermo rules, the orders of cycles strictly increases starting from the bulb.

Cells outlined with a cage have a digit that is equal to their cell's order. E.g. if the digit inside a cage is a 4, that cell is part of an order 4 cycle. (No negative constraint applies/not all possible cages are necessarily given)

Additional info:

I've gotten feedback that this ruleset can be tricky to wrap your head around, so I'm calling out a few insights which directly follow from the above definitions for clarity to make this more approachable.

  • Cycles cannot partially overlap. A cell is only ever part of a single cycle
  • The order of all unique cycles in a row always sums to 9.
  • A cycle can have an order of 1 if, and only if, the digit in a cell is the same as the cell's column number. This means you can remove some candidates in a row that would create an order 1 cycle in situations where you already know there are cycles in the row that sum to 9. For a specific example, if there's an order 9 cycle in a row, then column 1 in that row cannot be 1, column 2 cannot be a 2, column 3 cannot be a 3 etc.

Solution code: Row 1 + Row 2 (18 digits, no spaces)

Last changed on on 27. August 2022, 20:35

Solved by alisonsky, Kworb, efnenu, kublai, tesseralis, DVFrank, randomra, thoughtbyte, ICHTUES, Droi, Counterfeitly, tlepetit, cha, starwarigami, cdwg2000, Uhu, SKORP17, OGRussHood, tuturitu, salsais, Fractl, Sewerin
Full list

Comments

on 27. August 2022, 20:35 by SirSchmoopy
added walkthrough/solution guide now that the puzzle has been available for some time.

on 16. August 2022, 00:28 by ICHTUES
Very cool puzzle!

on 13. August 2022, 23:46 by thoughtbyte
Another great cycles puzzle, I liked the additional constraint of the caged cells. Very nice, thanks @SirSchmoopy!

Last changed on 12. August 2022, 03:21

on 12. August 2022, 03:21 by randomra
Tricky and fun throughout without any extremely difficult part. Wonderful puzzle!

on 11. August 2022, 00:09 by tesseralis
What a fun puzzle! This feels like a fine-tuned and perfected version of "bicycles" -- everything feels very tight and elegant.

on 10. August 2022, 10:14 by Kworb
Actually a really cool and elegant ruleset once you understand how it works. Great puzzle!

Difficulty:4
Rating:91 %
Solved:22 times
Observed:6 times
ID:000ARA

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