Off Topic but I asked a similar question in alt.math.recreational some time
ago and got this reply:
Start of my question *************************************
Please forgive me if this is too trivial for this group or too obvious.
If you take any number - say 820482 and reverse the digits to give 284028
there does not appear, (to me at least!), to be a numerical relationship
between them. However, if you subtract the smaller number from the larger
number, provided that the original number was not palindromic, the answer
will be a multiple of nine. I know that this works out but I cannot see how
there is a numerical relationship between the numbers.
Start of Rich's answer ************************************
It's a consequence of our number system being base 10. Consider a three
digit number with h in the hundreds place, t in the tens place, and u in the
units place. So for 472, h=4, t=7, u=2. The number represented by htu is
100h + 10t + u. Reversing it is the three digits uth which represents the
number 100u + 10t + h.
Assume the htu number is the larger of the two. Subtract them: (100h + 10t +
u) - (100u + 10t + h) = (100h - h) + (10t - 10t) + (u - 100u) = 99h - 99u >
= 99(h - u) = 9*11*(h-u)
So the difference between htu and uth will always be a multiple of 9, no
matter what h, t, and u are.
This is easily extended to numbers represented by any number of digits.
And this is why in beginning accounting you're taught that if an error is
divisible by 9, you've likely made a transposition error in your figures.
--
Rich Carreiro
End of Rich's Post***************************************
HTH
Sandy
