Logic Masters Deutschland e.V.

A new special role enters the stage of Chaconopia: The Politician

Sudoku on:
SudokuPad

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Rules:

1. Chaos Construction: The grid has to be devided into seven regions of orthogonally connected cells. Each row, column and region has to contain the digits 1-7 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 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 value of the cell N steps away in the direction of an arrow is given in the corresponding circle. N is the digit in the cell from which the arrow extends (Example: If r7c2 would be a 3 then the value of r4c5 would have to be 10.)

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.