Once the hidden pair and the pointing pairs are resolved, the puzzle solves smoothly with singles to the end. Total solving time for an experienced player: 12–18 minutes.
As you progress to harder puzzles, basic scanning will leave you with a partially filled grid where no obvious moves remain. This is when you must use advanced logic notation and elimination strategies. Pencil Marking (The Candidate Grid)
(10 marks) Design a more difficult variant of Sudoku 129 by modifying or adding givens (do not change grid size). Specify the new grid and state which advanced techniques (e.g., Swordfish, Nishio, coloring) would likely be required to solve it logically. Explain briefly why the variant increases difficulty.
If "129" refers to an index number (e.g., Puzzle #129 in a newspaper or app archive), it represents a milestone. In many curated collections, early puzzles (1–50) serve as introductory mechanics, while later puzzles introduce complex variants.
block sums to . This is especially helpful in variant puzzles to find a single missing digit in a nearly full house [28, 32]. Triple Tracking
Sometimes, the candidate tracking reveals that a specific number can only exist within two or three cells inside a single 3x3 box, and those cells happen to align in a straight horizontal or vertical line. Because the number must go into one of those cells to satisfy the 3x3 box rule, it will automatically occupy that row or column. You can therefore eliminate that number as a candidate from the rest of that entire row or column outside of that specific box. Tips for Improving Your Solving Speed
This logic extends directly to three cells. If three cells in a single row, column, or box contain a shared pool of three candidates (such as the numbers 1, 2, and 9), those three digits can be instantly cleared from any other empty cells in that sector. The candidates do not all need to be present in every single cell; they simply cannot exceed the designated trio. For example: Cell A: [1, 2] Cell B: [2, 9] Cell C: [1, 9]
This is essential for hard puzzles. If a number (e.g., 5) can only go in two cells in Row 2, and only in two cells in Row 8, and these cells form a rectangle (they align in Column 3 and Column 7), you can eliminate all other 5s from Columns 3 and 7. 6x6 Mini Sudoku #129 Example
While "129" is most often associated with the specific website brand, the numbers 1, 2, and 9 occasionally appear in specific Sudoku contexts: