I was reading about dyslexia (which I believe I have though I have never been diagnosed) when I came upon this strange statement:
When two adjacent numbers are transposed, the resulting mathematical error will always be divisible by 9 (e.g., (72-27)/9 = 5).
I tried transposing a number of numbers and they were, indeed, divisible by 9.
I'm terrible at math; it was always my worst subject (and consequently? my most disliked) though I had to use it multiple times every day in my work.
Could someone explain (as if to an idiot) why the above holds true?
(I did read that this site was all-purpose, including for beginners. Please forgive me if this is OT.)
$\endgroup$1 Answer
$\begingroup$Write the first number as $10 a + b$, and the second as $10 b + a$ (in your example, $a = 7$ and $b = 2$). Then
$$(10a + b) - (10 b + a) = 9a - 9b = 9(a - b)$$
is divisible by $9$.
$\endgroup$ 4
