MathDB

Let

N

be a positive integer. Brothers Michael and Kylo each select a positive integer less than or equal to

N

, independently and uniformly at random. Let

p_N

denote the probability that the product of these two integers has a units digit of

0

. The maximum possible value of

p_N

over all possible choices of

N

can be written as

\tfrac ab,

where

a

and

b

are relatively prime positive integers. Compute

100a + b

Problem Statement