Love the Sam Loyd Puzzles, but have a discrepancy on the keys puzzle.
The key sentence for me was "since 6910 multiplied by 7 does not equal 83452". This implies that if it did equal 83452, that the arrangement of keys would be correct. Solving it along this line, I took the factors of 83452, and found that 20863 multiplied by 4 does equal 83452, so that is my answer. Did I miss something???