I learned CE just as the first pocket calculators were being introduced (HP 35 $399.00). I did many a mile of road and railroad using pencil and paper. Unfortunately, I was never good with ink
The way to find a transposition of adjacent numbers is to look for a difference of nine (9). if the difference between the written number and the calculated number is 9, 90, 900 ..., there is a number transposition. (9 will mean the unit and tens columns, 90 will mean the tens column and hundreds columns, etc).
I saw the proof several times but in 40 years I have forgotten it. There were all sorts of tricks to find errors in transpositions in pre-calculator days. I recall when desk top calculators required a desk to themselves and costed several thousands of dollars.
Makes me feel old - geriatric.
I recalled one person saying that the more times you recopy the numbers, the more chance there is of errors.
Oh well, Maybe someone will remember to spread some of my ashes on Cumbres.
Doug vV