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It's not quite "just knowing". More like several half-conscious explanations occur to me at the same time. If the answers conflict I need to think about it carefully, if they're all the same, I'll trust it & feel that I "know" it.
Looking at what I just wrote... I suspect that me saying more is not helping for demystifying this.
I wonder if a more complex example would help clarify what happens in your head. E.g. how do you approach 2484+5839? Or 349753+935731?
Very differently, though still with some overlap: multiple instinctive approximate models, but then detailed step-by-step models for exact computation. Though the exact model will tend to be somewhat made up on-the-fly.
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