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You rolled 1 + 2 = 3
You lose
You rolled 4 + 4 = 8
point is 8
You rolled 6 + 2 = 8
You win
You rolled 3 + 2 = 5
point is 5
You rolled 2 + 5 = 7
You lose
**5.31
(
Financial: credit card number validation
) Credit card numbers follow certain pat-
terns. A credit card number must have between 13 and 16 digits. It must start with:
■
4 for Visa cards
■
5 for Master cards
■
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 number 4388576018402626):
1. Double every second digit from right to left. If doubling of 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 = 4
4
*
2 = 8
1
*
2 = 2
6
*
2 = 12 (1 + 2 = 3)
5
*
2 = 10 (1 + 0 = 1)
8
*
2 = 16 (1 + 6 = 7)
4
*
2 = 8
2. Now add all single-digit numbers from Step 1.
4
+
4
+
8
+
2
+
3
+
1
+
7
+
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 Step 2 and Step 3.
37
+
38
=
75
