refine wording

Author: tasxatzial

exercises/luhn/instructions.md

@@ -14,25 +14,23 @@ All other non-digit characters are disallowed.
 
 ### Valid credit card number
 
-```text
-4539 3195 0343 6467
-```
+The number to be checked is `4539 3195 0343 6467`.
 
-The first step of the Luhn algorithm is to double every second digit, starting from the rightmost (last) digit of the number and moving left.
+The first step of the Luhn algorithm is to start at the end of the number and double every second digit, beginning with the second digit from the right and moving left.
 
 ```text
 4539 3195 0343 6467
 ↑ ↑  ↑ ↑  ↑ ↑  ↑ ↑  (double these)
 ```
 
-If the result of doubling a digit is greater than 9, subtract 9 from that result.
+If the result of doubling a digit is greater than 9, we subtract 9 from that result.
 We end up with:
 
 ```text
 8569 6195 0383 3437
 ```
 
-Then sum all digits, and if the sum is evenly divisible by 10, the original number is valid.
+Finally, we sum all digits, and if the sum is evenly divisible by 10, the original number is valid.
 
 ```text
 8 + 5 + 6 + 9 + 6 + 1 + 9 + 5 + 0 + 3 + 8 + 3 + 3 + 4 + 3 + 7 = 80
@@ -42,25 +40,23 @@ Then sum all digits, and if the sum is evenly divisible by 10, the original numb
 
 ### Invalid Canadian SIN
 
-```text
-066 123 468
-```
+The number to be checked is `066 123 468`.
 
-Double every second digit starting from the rightmost (last) digit of the number and moving left.
+We start at the end of the number and double every second digit, beginning with the second digit from the right and moving left.
 
 ```text
 066 123 478
  ↑  ↑ ↑  ↑  (double these)
 ```
 
-If the result of doubling a digit is greater than 9, subtract 9 from that result.
+If the result of doubling a digit is greater than 9, we subtract 9 from that result.
 We end up with:
 
 ```text
 036 226 458
 ```
 
-Sum the digits:
+We sum the digits:
 
 ```text
 0 + 3 + 6 + 2 + 2 + 6 + 4 + 5 + 8 = 36