Logic Masters Deutschland e.V.

In a standard Sudoku grid of 9x9 cells, divided into 3x3 boxes of 3x3 cells each...

Normal Sudoku Rules Apply...

1. A digit is to be dropped into the center of the grid. From it the corners of ripples propagate outwards both diagonally (D) and orthogonally (O). See diagram. The sum of the digits in each ripple is referred to by its type (O or D) and its distance from the center.

2. All O Ripples as far as O6 are perfect squares plus one (e.g. 10 = 3x3+1), except O4 which is exactly a perfect square. (O7 and O8 are each prime. Digits outside the regular grid are all zeroes.) The Root of a ring is the square root of one less than the sum of the digits in that ring, except O4, which is the exact square root of the sum of the digits in that ring.

3. All D Ripples are prime numbers except D2, which is one more than O4 and one less than a prime.

4. In each D ring, there is no corner digit lower than that in its top left corner.

5. The digit representing a ring number only appears in a corner of that ring on two occasions. The digit dropped in the center never reappears in any corner.

6.Four different digits comprise the corners of D3, two of which are prime digits but none is a perfect square. 4 different digits comprise the corners of D4, Further, 4 different odd digits the corners of O2.

7. The Root of each O ring appears in one corner of that ring except in O4 (and those rings with corners beyond the standard grid (these being all zeroes))

8. O2 Root and O3 Root appear in their respective bottom corners.

9. O3 Root appears again in that ring as many times as allowed including the left corner. O4 Root also appears 4 times its respective ring including once in consecutive cells.

10. All digits that are perfect squares appear at the corners of O1 and again at the corners of D2. In O1 the sum of the top and bottom corner digits equals the digit in the right corner. In D2 the remaining corner digit is not prime either.

11. D1 corner digits increase anti-clockwise. D2 corner digits increase clockwise (while respecting Rule 4)

12. In the bottom right box, the prime digits appear in a 2x2 grid with the largest in the top left.

13. In one box, the perfect square digits are stacked in a column next to a stack of the digits which are neither perfect squares nor prime.

Happy Solving.