Logic Masters Deutschland e.V.

Creating Chaconopia puzzles with the new special role ‘Politician’ is proving to be quite complicated. But fortunately, I was successful once again and can now present this special creation.

Sudoku on:
SudokuPad

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Rules:

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

2. Roles: If certain conditions are met, cells can take roles that increase their value. The value of a cell with no role is it's digit. Role values and conditions are described below.

2.1 Role conditions and values (X = Digit in a cell)

2.1.1 Basic roles:
- Farmer (Value = 2X): To become a Farmer, a cell needs at least X cells including itself of its own region in the 3x3 area centered on the cell.
- Merchant (Value = 3X): To become a Merchant, there has to be at least one foreign region that occupies at least X orthogonally and/or diagonally touching cells of the considered cell.
- Diplomat (Value = 4X): To become a Diplomat, a cell has to be orthogonally and/or diagonally touched by at least X different other regions.

2.1.2 Special role:
- Politician: To become a Politician, no condition needs to be met. The value of a Politician cell is at least X. Additionally, the value of the Politician cell is increased by X for each orthogonal direction, in which the Politician cell is connected to a contiguous straight line of cells from its own region with a digit sum of X or higher.

2.2 Role assignation: Basic roles are automatically taken if their condition is met. If more than one condition is met, a cell takes the role with the highest value.
The Special role "Politician" may appear only once per region and can either be taken by a cell with no role or replace the Basic role of a cell. The Politician role is taken by the cell, that can achieve the highest absolute increase in value by becoming the Politician. In case of a tie, all cells involved could be the Politician and it has to be determined by the solver which of the cells is the Politician.

3. Clues:
- The product of the values of the cells along a red arrow have to equal the value in the attached circle.
- The sum of the values of the cells along a grey arrow have to equal the value in the attached circle.
- Values in cells seperated by a white dot must be consecutive (no negative constraint).
- Values in cells seperated by a black dot must be in 1:2 ratio (no negative constraint).
- The difference of the values in both pairs of cells seperated by a blue dot must be the same.

Have fun solving!

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Example: This is an 5x5 example picture to show how the Politician role is assigned to cells. White circles mark the Politician cell in a region. Basic roles obey the same rules as described above but are not marked:
- Region A: The cell with 3 is the only cell increasing its value by taking the Politician role. It can't take any Basic role but has is connected to one group of cells (below) increasing it's value as a Politician to 6. The cells with 1, 2, 4 all have Basic roles with at least the value they could reach by becoming the Politician.
- Region D: All four directions increase the Politician value of the cell with 1 so it's value is 1 + 4 = 5. It's Basic role would be Diplomat with a value of 4 but the increase of 1 is enough to become the Politician in that region as all other cells have Basic roles with at least the value they could have by becoming the Politician.
- Region B: In region B no cell can increase it's value by becoming the Politician. Therefore there is no Politician (Note: In bigger grids, this scenario becomes much less likely to appear.)
Regions C and E: Try to prove by yourself, why the indicated cells are the Politicians.