Inspired by the original T. Snyder’s “What If” article, I tried my hand at constructing a Sudoku problem whose difficulty increased as much as possible when a single element is removed, while retaining human solvability. This resulted in this pair of puzzles, one of which can be used as an introduction to Sudoku, while its near twin requires considerable experience to complete in a logical manner. Scanraid’s grader assigns them ratings of Gentle(27) and Tough (151), which concurs with my gut.
The puzzle below is the difficult one, while the easy version, and some spoilery commentary follows after the break.
Turning it into a trivial puzzle requires the addition of just one given ,though the grid adds two for symmetry's sake; either one suffices, but giving both does not further diminish the problem (well if it did, there wouldn't be any problem left).
This grid was designed to have some interesting properties, which any casual observation of the grid will reveal. The less obvious one is that nth box contains n in its nth position (Well, it did until I removed the 5 from the centre of the centre box, for reasons discussed below). The grid is symmetric, and symmetric givens add up to 10, hence the puzzle name (again, with a singular exception that is rather useful for achieving a unique solution, and helped in late stage solving). Border pairs also add up to 10.
So why did the five in the centre have to go? It hardly affects the solution path in either puzzle, and is trivially easy to add in both. However, it had to go because I felt all the patterns could potentially lead a solver to guessing the mostly ordered contents of the centre box. Now, guessing could be very good for the hard version solver, as the difficulty dropping digits conform to the most obvious guess, but very bad for the novice solver, as there is a single transposition in there, potentially turning their grid into a smudgy mess. So I opted for that limited amount of obfuscation, just to be on the safe side. I'm sure computers don't fret like that when they design puzzles. Other than that, I'm pretty happy with the number, mix, and order of useful techniques for both puzzles. I did try to make use of a technique I typically avoid in the hard puzzle, so some potential for mis-estimation of difficulty exists in the final steps of the harder version. I'd like to hear how smooth you found the solving path of both.
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