Tricky average problem - Iran First Round 2018, P8
Source:
March 7, 2021
combinatorics
Problem Statement
The license plate of each automobile in Iran consists of a two-digit and a three-digit number as well as a letter of the Persian alphabet. The digit is not used in the two numbers. To each license plate, we assign the product of the two numbers on it. For example, if the two numbers are and on a license plate, the assigned number would be . What is the average of all the assigned numbers to all possible license plates?