MathDB

For any finite non empty set

X

of integers, let

\max (X)

denote the largest element of

X

and

|X|

denote the number of elements in

X

. If

N

is the number of ordered pairs

(A, B)

of finite non-empty sets of positive integers, such that

\begin{aligned} & \max (A) \times|B|=12 ; \text { and } \\ & |A| \times \max (B)=11 \end{aligned}

and

N

can be written as

100 a+b

where

a, b

are positive integers less than 100 , find

a+b

Problem Statement