Just For Fun / Mini-Sudoku/Logic Puzzle Hybrid

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Can you name the answers to this logic puzzle?

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Each cell contains an integer between 1 and 6 (inclusive). As with Sudoku, each row and each column cannot contain more than one instance of the same number. However, unlike Sudoku, there are no cages that are guaranteed to contain only one instance of each number. When a number is "one away from another number numerically", it means that the difference between those two numbers is 1. Adjacency includes diagonals. This can be done without guessing.
A1





B1





C1





D1





E1





F1





A2





B2





C2





D2





E2





F2





A3





B3





C3





D3





E3





F3





A4





B4





C4





D4





E4





F4





A5





B5





C5





D5





E5





F5





A6





B6





C6





D6





E6





F6





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