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I decided to work my way through Simon Tatham's puzzle collection to broaden my puzzling skills, and have reached the game Dominosa

I have a subboard below, where I've eliminated the possibility of 9/3 and 9/5 dominoes being in this area.

2385/5990/5927/3565

May I infer that the 9/9 domino is the left half of the central 2x2 square, rather than the top half, and additionally that the right half is not a single 9/2 domino?

My thought is that if it were otherwise, the center square would be ambiguous in orientation between the horizontal and the vertical, but I'm not certain if such ambiguity is forbidden.

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    $\begingroup$ If ambiguity is indeed not possible (which seems the most logical to me) your conclusion seems correct to me. But I think only the creator of that website can answer that. He is the only one that knows if any ambiguity is possible. $\endgroup$ – Ivo Beckers Feb 27 '17 at 14:58
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In grid deduction puzzles, there is a unique solution to each puzzle. What you're using is known as "unique solution logic", using the meta-fact that the puzzle has a unique solution. There's nothing wrong with using it, but many people prefer not to do so in human-designed puzzles because it circumvents the logical path set by the designer, which could be more entertaining.

However, this is only valid if the puzzle is guaranteed to have a unique solution, and the algorithm used by Tatham to generate puzzles may not check for uniqueness. If so, this deduction would be invalid.

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