29 (Financial: credit card number validation) Credit card mumbers follow certain patterns it must have between 13 and 16 digits, and the number must start with: 4 for Visa cards 5for MasterCard creditcards 37 for American Express cards 6 for Discover cards In 1954, Hans Luhn of IBM proposed an algorithm for validating credit card num- bers. The algorithm is useful to determine whether a card number is entered cor- rectly or whether a credit card is scanned correctly by a scanner. Credit card numbers are generated following this validity check, commonly known as the Luhn check or the Mod 10 check, which can be described as follows (for illustra- tion, consider the card number4388576018402626): 1. Double every second digit from right to left. If doubling bf a digit results in a two-digit number, add up the two digits to get a single-digit number. 4388576018402626 2.2 4 2.2 m 4 4.2 m 8 1 2 m 2 5.2 a 10 0 1) 4 2 8 2. Now add all single-digit numbers from Step 1. 4 8 2 3 1 7 t 8 37 3. Add all digits in the odd places from right to left in the card number. 6 6 0 8 0 7 8 3 38 4. sum the results from Steps 2 and 3. s. If the result from step 4 is divisible by 10 the card number is valid. otherwise, it is invalid. For example, the number 4388576018402626 is invalid, but the number 4388576018410707 is valid