Snooker
(Published on 10. January 2023, 12:08 by Tobias Brixner)
Puzzle links: Play on CTC SudokuPad or f-puzzles.
Rules: Clear the Snooker table (shaded green). You just potted the last red and must now pot one of the colored balls (2-7) which will return once to its position. Then, pot all balls sequentially in ascending order.
Normal Sudoku rules apply, i.e., place the numbers 1-9 once each into each row, column, and 3×3 box.
A ball can be potted by placing the cue ball (digit 8) such that a straight line from its center to the object-ball center points exactly at the pocket center (gray circle). Each cue-ball position is different. The cue ball may not be placed onto a pocket or outside the table.
Draw a path through orthogonally connected cells passing all cue-ball positions in chronological potting order. Between successive 8s, the path does not change direction more than twice. It does not cross over pockets or given digits and does not leave the table. It must contain the white lines. It may touch itself orthogonally. No cell is passed twice.
Each path segment between successive 8s forms a separate entropic line, i.e., any set of three sequential cells must contain a low (L = 1,2,3), middle (M = 4,5,6), and high (H = 7,9) digit. Digits may repeat on a line if allowed by other rules. The start entropy type (L,M,H) after an 8 as well as the entropic order is the same for all segments when proceeding chronologically, even for segments shorter than three cells.
Three of the six cages collect pocketed balls: The sum of digits in the cage is the same as the sum of all ball digits potted into the embedded pocket. For the other cages, no such restriction holds.
Example: In the following partially filled grid, the green ball (3) is potted twice into the bottom right pocket, first from R6C2 and then from R7C4, and the potted total of 3+3=6 respects the cage rule of digits 4+2=6. Then the pink ball (5) is potted into the upper right pocket, with the corresponding cage being one of those not fulfilling the total-sum rule. (In the puzzle, a different potting order is required.) Note that the first path segment changes direction once, and the second segment twice. In this example, green is potted first, rather than pink. This can be deduced from the required identical order and starting type of entropies. Starting with the 8 in R6C2, the next digits on the path are 2=L and 9=H, and the same order is fulfilled in the next segment, i.e., first 1=L (which could also be 2 or 3), then 9=H (which could also be 7), and then 5=M (which could also be 4 or 6). If pink were potted first, the entropic order would be M=5, H=9, L=1, and the next segment (in R7C3) would again have to start with M, but it is a 9 instead.
Background: Snooker is a cue sport played on a rectangular table covered in green cloth, with six holes ("pockets") of which four are located in the corners and two in the middle of each long side. Summarizing the essential rules, a player hits the white "cue ball" with the tip of their cue. The cue ball in turn must hit an "object" ball, with the goal to "pot" the object ball into a pocket, i.e., make it fall through one of the six holes. First, a red ball (counting 1) has to be potted. If successful, any of the "colored" balls (yellow = 2, green = 3, brown = 4, blue = 5, pink = 6, or black = 7) is potted next, and then again a red ball and any colored ball alternatingly.
Colored balls return to designated spots on the table when potted, while red balls do not. When the last red ball is potted, the player has one last choice of potting any colored ball, which returns once more, and afterwards the colored balls must be potted in order of increasing value, starting with yellow. At this stage of the game, colored balls do not return onto the table. At the end, the player who scored more points wins a "frame".
The colors, values, and initial positions of the "balls" in this puzzle correspond roughly to those in a real Snooker game. In a real game, however, players generally do not want to hit object balls "straight on" because that would restrict the cue-ball movement; players rather want to hit object balls at an angle such that they can better control the subsequent cue-ball movement with the goal to place the cue ball in an ideal spot for the next shot. In the present puzzle, the situation is adapted to the simplified Sudoku grid to provide a unique solution path. Thus, also the puzzle's "cue-ball path" is not physically realistic but rather symbolizes the logical potting order. The cages of the puzzle correspond to the "ball rails" that are mounted under pockets of real Snooker tables and collect the potted balls.
Solution code: Column 1 (digits from top to bottom without spaces)
Comments
on 7. May 2024, 17:22 by davidemsa
I liked this one a lot. As a snooker fan, I think you got the theme down perfectly. I felt like I was playing with snooker and geometry for a while, that was fun, the sudoku only came after.
on 25. February 2023, 22:50 by Zombie Hunter
Great concept executed with tremendous skill. Wonderful puzzle.
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Thank you so much for the kind comment! - TB
on 25. February 2023, 22:49 by Zombie Hunter
Great concept executed with tremendous skill. Wonderful puzzle.
on 11. January 2023, 09:15 by tryote
very nice!!
