Logic Masters Deutschland e.V.

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Rules:

Normal sudoku rules apply.

x-sums: Numbers outside the grid show the sum of the first x digits from that direction, where x is the first of those digits.

n-cycles: Select a digit a in one of the rows or columns. Then go to position a of that row/column, which contains the digit b. Then go to position b of that row/column, which contains the digit c, and so on. An n-cycle is the set of n unique digits in this sequence. (See example below.)

Square: A cell containing a square and the digit n indicates that row has an n-cycle which includes the digit n in it.

Circle: A cell containing a circle and the digit n indicates that column has an n-cycle which includes the digit n in it.

Not all squares/circles are necessarily given.

Example:

The 2 takes us to the 5 in the 2nd position, which takes us to the 1 in the 5th position, which takes us back to the 2 in the 1st position. Therefore the green digits 2, 5, and 1 comprise a 3-cycle. The digit 3 is not part of this 3-cycle, so its cell cannot contain a square.

The 7 takes us to the 9 in the 7th position, which takes us to the 4 in the 9th position, which takes us to the 3 in the 4th position, which takes us back to the 7 in the 3rd position. Therefore the blue digits 7, 9, 4, and 3 comprise a 4-cycle. The digit 4 is part of this 4-cycle, so its cell can contain a square.

The 6 is already in the 6th position, so it is a 1-cycle. The same is true for the 8 in the 8th position. The digit 1 is not part of either 1-cycle, so its cell cannot contain a square.

Solve on Cracking the Cryptic

SPOILER ALERT Walkthrough of Solution

Puzzle: