This puzzle was created for a speed-setting event on the Cracking the Cryptic Discord server. I immediately had the idea for how to determine the set of numbers to be used and, unbelievably, the construction of the actual puzzle didn't require any backtracking at all, with the first placement of clues I settled on producing a puzzle that could be disambiguated with only two additional clues in an elegant way. All in all, the whole puzzle took about 10 minutes to write, which is miraculous.
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Rules
Place a number from 1 to 9 into each empty cell so that every number that appears in the grid appears in every row, column and bold-outlined region exactly once. The exact set of numbers to be used must be determined by the solver.
There are some circles marked with a number and an operation. Around such a circle, both pairs of diagonally opposite cells must contain numbers that result in the number shown when the operation is applied. If an operator symbol is replaced by a question mark, then the operation is allowed to be different for the two pairs of numbers around the circle.
An "E" or "O" on a circle indicates that all four of the surrounding digits are even or odd, respectively.
Difficulty: 4/10
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