Sudoku-Like Puzzle

Sudoku-Like Puzzle Rules

General Puzzle Structure

• The puzzle has 40 hexagonal cells arranged in a trapezoidal layout:
  • Rows of 6, 7, 8, 9, and 10 cells (from top to bottom).
• Each cell can contain an integer from 1 to 10.
• All values must be placed such that:
  • Each integer (1-10) appears exactly 4 times across the entire grid.

Block Constraints

• The grid is divided into 8 blocks (each with 5 cell indices).
• For each block:
  • No duplicate values.
  • Each block must contain at least one prime number (2, 3, 5, or 7).
  • Every prime in the block must be adjacent (a common edge) to an even number.
  • Exception: value 2 is exempt from this requirement if it is in one of the two special blocks (see below).
  • The sum of the values in each block must be unique (no two blocks can have the same total).

*Special Block Rule: {2, 3, 5, 7, X} *

• Exactly two blocks must contain the set {2, 3, 5, 7, X}.
• In one of these blocks, X must be odd; in the other, X must be even.
• In these blocks:
  • The 2 is exempt from needing to be adjacent to an even number.

Adjacency Rule

• Two cells are adjacent if they have a common edge.
• For every prime value (except 2 in special blocks), there must be in the same block an adjacent cell that holds an even value.

Alignment Rule

• There is an alignment mapping across the 40 cells.
• Cells that are "aligned" (e.g., in the same visual row, column, or diagonal) must not contain duplicate values. Note: Each cell usually has 6 (not 3) alignments, 3 along the edges and 3 along the vertices.

No Duplicate Values

• No repeated values within:
  • Any block,
  • Any alignment group,
  • The global digit distribution (each digit used exactly 4 times)

The puzzle has a verified solution.