Problem
NT-B1-M10-P012 Rearranged Digits
#12
★★☆☆☆ Level 2 of 5
Prove that the difference of two numbers formed from the same decimal digits is divisible by \(9\).
Such numbers have the same digit sum.
Each number is congruent to its digit sum modulo \(9\). The digit sums are equal, so the two numbers are congruent modulo \(9\). Therefore their difference is divisible by \(9\).
Standard idea, now in proof form.