The first four digits of the six-digit initial password for a shopper's card at a certain grocery store is the customer's birthday in day-month digit form. For example, 15 August corresponds  to 1508 and 5 March corresponds to 0503. The 5th digit of the initial password is the units digit of seven times the sum of the first and third digits, and the 6th digit of the initial password is the units digit of three times the sum of the second and fourth digits. What month, and what day of that month, was a customer born whose initial password ends in 16?

(1)The customer's initial password begins with 21, and its fourth digit is 1.

(2)The sum of the first and third digits of the customer's initial password is 3, and its second digit is 1.