Coding Challenge 2 A credit (or debit) card, of course, is a plastic card with which you can pay for goods and services. Printed on that card is a number that’s also stored in a database somewhere, so that when your card is used to buy something, the creditor knows whom to bill. There are a lot of people with credit cards in this world, so those numbers are pretty long: American Express uses 15-digit numbers, MasterCard uses 16-digit numbers, and Visa uses 13- and 16-digit numbers. And those are decimal numbers (0 through 9), not binary, which means, for instance, that American Express could print as many as 10^15 = 1,000,000,000,000,000 unique cards! (That’s, um, a quadrillion.) Actually, that’s a bit of an exaggeration, because credit card numbers actually have some structure to them. Credit card numbers also have a “checksum” built into them, a mathematical relationship between at least one number and others. That checksum enables computers (or humans who like math) to detect typos (e.g., transpositions), if not fraudulent numbers, without having to query a database, which can be slow. Of course, a dishonest mathematician could certainly craft a fake number that nonetheless respects the mathematical constraint, so a database lookup is still necessary for more rigorous checks. Well, credit cards use an algorithm invented by Hans Peter Luhn of IBM. According to Luhn’s algorithm, you can determine if a credit card number is (syntactically) valid as follows:

• Multiply every other digit by 2, starting with the number’s second-to-last digit, and then add those products’ digits together.
• Add the sum to the sum of the digits that weren’t multiplied by 2.
• If the total’s last digit is 0 (or, put more formally, if the total modulo 10 is congruent to 0), the number is valid! let’s try an example with David’s Visa: 4003600000000014 For the sake of discussion, let’s first underline every other digit, starting with the number’s second-to-last digit: 4003600000000014
• Okay, let’s multiply each of the underlined digits by 2: (12) + (02) + (02) + (02) + (02) + (62) + (02) + (42)
• That gives us: 2 + 0 + 0 + 0 + 0 + 12 + 0 + 8
• Now let’s add those products’ digits (i.e., not the products themselves) together: 2 + 0 + 0 + 0 + 0 + 1 + 2 + 0 + 8 = 13
• Now let’s add that sum (13) to the sum of the digits that weren’t multiplied by 2 (starting from the end): 13 + 4 + 0 + 0 + 0 + 0 + 0 + 3 + 0 = 20
• Yup, the last digit in that sum (20) is a 0, so David’s card is legit! So, validating credit card numbers isn’t hard, but it does get a bit tedious by hand. Let’s write a program. For this challenge, you are required to write a program that prompts the user for a credit card number and then reports whether it is a valid American Express, MasterCard, or Visa card number, per the definitions of each’s format below. For simplicity, you may assume that the user’s input will be entirely numeric (i.e., devoid of hyphens, as might be printed on an actual card) and that it won’t have leading zeroes. Consider the below representative of how your own program should behave when passed a valid credit card number:
• American Express numbers start with 34 or 37
• MasterCard numbers start with 51, 52, 53, 54, or 55
• Visa numbers start with 4 Submit your code with your output commented out at the end of your code. You are free to use C, C++, C#, Python or Java to implement this program. Please upload your code to GitHub and submit the GitHub link for the same in a word document with your name on Canvas under the ‘Assignments’ tab. ** Note: If you have any questions regarding this coding challenge, feel free to post it in the weekly-challenge channel in discord! Good Luck and Have Fun!