Divisibilityhard
0:00.0

Let N=(1a2b3c)8N = (1a2b3c)_8 be a six-digit number written in base 8, where a,b,ca, b, c are digits in base 8. If NN is divisible by both 99 and 77, what is the maximum possible value of the base-10 sum a+b+ca + b + c?