Question 15
Luhn algorithm: reverse the digits; sum odd-position digits as $A$; double even-position digits and sum digits of their products as $B$. Validity requires $A + B$ divisible by $10$. Example $4634 8932 1298 2767$ reverses to $7672 8921 2398 4364$ with $A = 45 , B = 45$. The valid string $2853 00 QP P = 003 6002$ has digits $P \le Q$. How many pairs $\left(P , Q\right)$?