Outside clues and empty grids are always my favourite Sudokus to construct. It's generally a bit of a struggle to get them to turn out unique or even create an opening. This one was a bit of a struggle to get unique as my final clue had to settle about 35 cells. There were a few options that got pretty close but would end up having no solution. This was the only one I could find that settled the uniqueness issue. There was a second option that I thought had worked, but then I realised the clue didn't actually have to be in that configuration and thus there were many more solutions. The puzzle itself is not overly hard as the clues give you a lot of information from the start and the clue I used for uniqueness is already helpful far earlier than it was in my construction.
Rules for Sudoku
In this Sudoku, the numbers on the outside indicate the product of the highest and lowest digit in the first three cells of that row or column when looking from that side.
That's pretty fun! It was tough for me to keep remembering that it was the highest and lowest digit forming the product, not all three digits and not any two arbitrary digits. Somehow that didn't feel like a "natural" rule to me. But it did lead to some nice logic.
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