Logic Masters Deutschland e.V.

Following on from “The Beginning” and “The Escalation”, here is “The Pinnacle” – the conclusion and climax of this first trilogy of 9x9 puzzles based on the concept.

Sudoku on:
SudokuPad

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Rules:

Chaos Construction: The grid has to be divided into nine regions of orthogonally connected cells. Each row, column and region has to contain the digits 1-9 once each.

Duels: At each region border, a duel takes place between the adjacent regions. To determine the outcome, for both sides the contiguous sequences of cells extending perpendicular from the region border to the next region border or the edge of the grid are compared. The region whose sequence of cells has the higher sum of digits wins the duel. An award of X points for the winning region and a penalty of -X points for the defeated region are taken by the cells touching the region border where the duel takes place. X equals the number of cells in the sequence of the defeated region. If the sum in both sequences is equal it's a tie and no points are awarded.

Clues:
- An arrow between cells marks a region border and points to the defeated region in the duel at that border. A diamond marks a region border where the outcome of the duel is a tie. Not all arrows and diamonds are necessarily given.
- A small number in the bottom-right corner of a cell gives the total points this cell wins/loses in the duels at its up to 3 region borders. If a letter is given, the total has to be determined by the solver. All cells with the same letter have the same total.

Have fun solving!

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Example: This is the solution to a 5x5 example puzzle. For the arrows shown, the points gained or lost are indicated to illustrate how duels work. For example, the central cell loses the duel at its left-hand region border (sum of 5 [4+1] is less than sum of 8 [5+3]) and receives 2 minus points, as the sequence of cells in the losing region (blue) consists of 2 cells. The cell wins the duel at its upper region border (4 against 2) and gains 1 positive point for this, as the losing region (green) contributes only one cell to the duel. At the lower region border, the result is a tie (4 = 3 + 1). This results in a total score of -2 + 1 + 0 = -1 for the cell in question.