Question 109
Bank is planning to produce and grant a special credit card to its loyal customers. Each of these credit cards has a unique ID-number that has 16 digits and satisfies the following properties:
(i) The first four digits of the ID-numbers is fixed and is equal to 2024.
(ii) For each pair of cards their corresponding ID-numbers must differ in at least two digits.
Prove that the maximal possible number of cards that can be produced is $10^{11}$.
(i) The first four digits of the ID-numbers is fixed and is equal to 2024.
(ii) For each pair of cards their corresponding ID-numbers must differ in at least two digits.
Prove that the maximal possible number of cards that can be produced is $10^{11}$.