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1023 = 2^10 - 1. It would have taken all the 10 fingers.

1023=2^10, 0-indexed.

but in this case thre is no patent at index 0 (or some other). Don't know if this was a subtle choice

Even 0 indexed, 2^10 patents is still 1024 patents.

You missed their secret weapon, the zeroth patent.

1023 = 0b1111111111