The twins Maxim & Minerva independently replaced the letters in the word

**KANGAROO** upon the following rules:

1. Similar letters are replaced by the same digit

2. The resulting 8-digit number must be divisible by 11.

3. Maxim had to choose the maximal qualifying number, Minerva - the minimal.

Comparing their correct answers they've found out that a certain letter in the word **KANGAROO** was replaced by the same digit in their independent answers.

Specify **WHAT** letter and explain **WHY.**

I'll assume the basics: no leading zeros and each letter represents a distinct base 10 digit.

For KANGAROO to be a multiple of 11, the difference (K+N+A+O)-(A+G+R+O) must also be a multiple of 11. This difference simplifies to K+N-(G+R) = 0 mod 11.

Let Minerva's first three digits be the absolute minimum with the assumptions previously mentioned. Then KAN=102. This implies 3-(G+R) = 0 mod 11 with G and R limited to {3,4,5,6,7,8,9}. The smallest G can be in this equation, given the set of digits available, is G=5, which makes R=9. Then Minerva has KANGAROO=10250933.

Similarily, Maxim's first three digits are KAN=987. This implies 16-(G+R) = 0 mod 11 with G and R limited to {0,1,2,3,4,5,6}. Then the largest G is 5 with R=0. Then Maxim has KANGAROO=98758066.

Then comparing the numbers is simple:

KANGAROO

10250933

98758066

The letter/digit they have in common is **G=5**.