Twin Corresponding Sudoku consists of two side-by-side, seemingly independent, standard 9x9 Sudoku boards on the left and right. On the surface, they do not overlap with each other, but in fact, their final answers are logically locked together by an extremely clever"digital password mapping".
There is a one-to-one correspondence between numbers (i.e. password shuffling) between the two Sudoku solutions. For example, if all "1"s on the left side of the disk correspond to "7" at the same position on the right side of the disk, then all "2"s on the left side must correspond to another fixed number (such as "4") on the right side, and this mapping is two-way binding and unique.
(xth row, yth column) is the number A, and the answer to the right disk at the exact same coordinates (xth row, yth column) is the number B. This means that a pair of mappings A on the left ↔ B on the right is established. Left A ↔ Right B is established through reasoning, then all the grids on the left disk that are filled with A must be filled with B at the same coordinate positions on the right disk; vice versa, all B on the right disk must be filled with A at the same coordinate positions on the left side. Tip 1: Find the "deciphering point" to establish a codebook
The first step in solving the problem is not to crazyly deduce a single disk, but to establish a "codebook". If you use basic Sudoku skills to solve the answer to a certain grid on the left side of the board (assuming it is 3), and at the same time you find that the grid with the same coordinates on the right side of the board happens to be the given known clue 8, congratulations, you have cracked the first password: Left 3 ↔ Right 8! Quickly write down this mapping relationship on paper.
Tip 2: Use the codebook for "cross-border airdrop"
This is the most enjoyable part of this variant. Once you master the password of Left 3 ↔ Right 8, you can immediately convert all known or deduced "3" on the left side of the disk into "8" at the corresponding coordinate position on the right side; at the same time, convert all "8" on the right side into "3" at the corresponding position on the left side. This is equivalent to two boards "airdropping" known clues to each other, which can break the deadlock instantly!
Tip 3: Trial and error lightning protection with dual-disk mirroring
Sometimes you can't directly get the number of a grid, but you can use the mapping relationship to eliminate candidate numbers. For example: you guess that a certain cell on the left may be 5. According to the codebook you already have, Left 5 corresponds to Right 9. But you take a look at the same coordinates on the right side of the disk and find that the counterpart or house in that position already has a 9, causing a conflict. This means that 9 cannot be filled in on the right, so the square on the left cannot be 5! This method of using "mirror clones" to cross mine is extremely efficient.
Example picture: The coordinates of the left and right disks are completely consistent, and there is a unique global mapping relationship between the numbers
A: Not necessarily! "One-to-one correspondence" means: the left set {1 to 9} is reshuffled as a whole and mapped to the right set {1 to 9}. If Left 1 → Right 5, then Right 5 → Left 1 is absolutely true. However, the 1 on the right will correspond to who on the left, and you need to decipher it separately. It may correspond to left 7, or it may exactly correspond to left 5 (but this is not necessary).
A: Absolutely impossible. When designing the question, the question maker deliberately "encrypted" the key clues needed to pass the level and divided them into two boards. There are too few known numbers for any single disk, and relying on a single disk will definitely lead to failure. You have to create a codebook, "translate" back and forth between the two boards and carry clues to each other before you can finally piece together the complete solution.
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