Logic Masters Deutschland e.V.

Puzzle links: Play on CTC SudokuPad (with solution check) or f-puzzles.

Rules: Normal Sudoku rules apply, i.e., place the numbers 1-9 once each into each row, column, and 3×3 box.

All cells orthogonally or diagonally adjacent to a circle form an associated CIRCLE. For a circle at the edge, assume that the two associated CIRCLE edge cells are connected around the circle outside of the grid.

Each circled number indicates the length of the longest sequence of increasing digits on the surrounding CIRCLE, either clockwise or counterclockwise, but not necessarily the larger of the two.

No digit appears in more than two circles.

One cage contains the number of clockwise and the other cage the number of counterclockwise CIRCLES.

Example: Red lines in the example indicate CIRCLES. Assume that the digits on the CIRCLE around R4C1 are determined. Then, the longest clockwise sequence of increasing digits is 135 from R3C1 to R3C2 to R4C2 with length 3, and the longest counterclockwise sequences are 14 from R3C1 to R5C1 and 15 from R5C2 to R4C2 with length 2. Both 2 and 3 are valid options for R4C1 indicating that it is not necessarily the higher number between the two senses of rotation of a CIRCLE that is entered into the associated circle. The sense of rotation must be determined by further logic. Note that digits may repeat on a CIRCLE if allowed by other rules (such as 1 here). Digits may also repeat between circle and CIRCLE (such as possibly 3 here).

Hints: These help you getting started. Highlight as much text as you like to reveal clues stepwise.

Question 1: What is the minimum number that can appear in any circle?

Answer 1: 2. No circular sequence can just decrease. At one point it has to "wrap back" to the initial value such that at least two successive digits always increase.

Question 2: What is the maximum number that can appear in the corner circles?

Answer 2: 3. There are not more cells on the CIRCLE.

Question 3: Which numbers go into the edge circles?

Answer 3: 4 and 5 according to the minimum and maximum rules already derived and the fact that all allowed 2s and 3s are already used up.

Question 4: What is the maximum for the circle in R2C8 (and analogously, for R8C2)?

Answer 4: 6. A second 2 or 3 has to appear in R2C7, R3C7 or R3C8, and thus there is no room for a longer CIRCLE sequence between the 2/3 cells even if they are at a maximum distance.

Question 5: Given the derived minimum digit for R5C8, what is the order of the circled numbers in R4C9 and R5C9?

Answer 5: 4 above 5, making R5C8 clockwise. Counterclockwise, it would not be possible to reach a minimum sequence length of 7.