Logic Masters Deutschland e.V.

This puzzle introduces a novel twist on Japanese Sums, by combining them with X-Sums. The title comes from the requirement to divide the grid into regions that each have either nine or five cells.

• Chaos Deconstruction:
  Locate nine regions of nine orthogonally connected cells in the grid and fill each cell with a digit from 1-9 such that no digit repeats in a row, column or region.
• Pentominoes:
  Cells outside of the regions must form pentominoes (orthogonally connected blocks of five cells). Shade these cells and fill every cell of each pentomino with the letter associated with its shape. Every pentomino must contain a different letter. Pentominoes may not touch each other orthogonally or diagonally.
• Japanese X-Sums:
  Clues outside the grid give a list of X-sums clues in order. The first cell of each group of unshaded cells in each row/column from the direction of the clues begins a new X-sum, summing the digits in the first X cells from that cell, including itself, where X is the value in that cell. Shaded cells are included in the count of cells, but are treated as zero value. If the count of cells would carry a clue beyond the grid boundaries, the clue is invalid and is labelled X.
• Liar Cipher:
  In each row/column, two sets of clues are given on the left/top and right/bottom of the grid. In each case, one set is true and the other is false. In these clues, each digit from 0-9 is encoded by a different letter from A-J. A ‘?’ may be replaced by any digit, but the first digit of a clue must not be 0. A ‘...’ represents any number of additional valid or invalid clues, possibly none. Invalid X-sums clues, labelled with X, are not encoded by the cipher.

A 6x6 example puzzle is provided below to explain the correct way to interpret Japanese X-Sums. In the example there are four regions of five cells each, tetrominoes are used for shaded regions and the liar cipher rule is discarded.

Solve Example on SudokuPad

Solve Example on Penpa

In both the example and main puzzle, all digits and letters must be filled in to trigger answer check (including the cipher in the main puzzle). This requires Letter Tool on SudokuPad, while Penpa can use Sudoku mode with Caps Lock turned on, or Number mode. In Penpa all edges of regions and pentominoes must also be drawn and the pentominoes must be shaded grey or black.

Small tetromino/pentomino grids are provided in the bottom right corner of each puzzle as a reminder of possible shapes and their associated letters. A larger image of possible pentomino shapes for the main puzzle is provided below.

Solve on SudokuPad

Solve on Penpa

This puzzle was constructed for Gliperal in the 2023 Secret Satan puzzle exchange. Having previously constructed for Gliperal in the CTC Discord 2021 Secret Santa, I wanted to create a complex puzzle combining elements of multiple genres that I wasn't experienced enough to construct when I made Grotto Spelunking and The Toppling Tree.

After experimenting with an idea for a deconstruction puzzle with 3x3 regions that divided the remaining cells into unique pentominoes, I was forced to conclude that this was probably impossible. That led to chaos deconstruction, which could work quite easily, while the Japanese X-Sums idea came from a suggestion of twists on variants such as bending X-sums. After playing around with the rule for a while I came up with some interesting logic, which worked well when combined with the liar cipher element to allow solvers to discover what is and isn't possible with this ruleset while solving the puzzle.

Solve video links in hidden comments: Gliperal