In the word KANGAROO Bill and Bob replace the letters by digits, so that the resulting numbers are multiples of $11$. They each replace different letters by different digits and the same letters by the same digits ($K \not = 0$). Bill obtains the largest possible such number and Bob the smallest. In both cases one of the letters is replaced by the same digit. Which digit is this?
Please give me a hint on the answer or ways to approach this question.