• 884

## Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

## Goal

Most payment card numbers are 16 digits long. The leftmost 6 digits represent a unique identification number for the bank who has issued the card. The next 2 digits determine the type of the card (e.g., debit, credit, gift). Digits 9 to 15 are the serial number of the card, and the last digit is used as a control digit to verify whether the card number is valid. Hence, if somebody enters the card number incorrectly, there is a high chance that a payment software can easily determine it.
Most cards use an algorithm invented by Hans Peter Luhn, a nice fellow from IBM. According to Luhn’s algorithm, you can determine if a credit card number is (syntactically) valid as follows:

1.Double every second digit from right to left. If this “doubling” results in a two-digit number, subtract 9 from it get a single digit.
2.Now add all single digit numbers from step 1.
3.Add all digits in the odd places from right to left in the credit card number.
4.Sum the results from steps 2 & 3.
5.If the result from step 4 is divisible by 10, the card number is valid; otherwise, it is invalid.
for example:

Test 1:
`4556 7375 8689 9855`

1.
`5*2 9*2 8*2 8*2 7*2 7*2 5*2 4*2`

`10 18 16 16 14 14 10 8`

`1 9 7 7 5 5 1 8`

2.
`1+9+7+7+5+5+1+8=43`

3.
`5+8+9+6+5+3+6+5=47`

4.
`43+47=90`

The number is valid

Test 2:
`4024 0071 0902 2143`

1.
`4*2 2*2 0*2 0*2 7*2 0*2 2*2 4*2`

`8 4 0 0 14 0 4 8`

`8 4 0 0 5 0 4 8`

2.
`8+4+0+0+5+0+4+8=29`

3.
`3+1+2+9+1+0+4+0=20`

4.
`20+29=49`

Therefore the number not valid.
So, validating credit card numbers isn’t hard, but it does get a bit tedious by hand.

Your task is to read several card numbers from the input, and determine whether each one is a valid card number or not.
Input
Line 1: An integer N for the number of cards to verify.
Next N lines: One line for each card to verify. Each test is consisting of four space-separated 4-digit strings.
Output
N lines: For each test case, output a line containing YES or NO depending on whether the card number is valid or not, respectively.
Constraints
Example
Input
```2
4556 7375 8689 9855
4024 0071 0902 2143```
Output
```YES
NO```

A higher resolution is required to access the IDE