I will do #1, as you are supposed to post one problem per post.  You can use this as a template for problem #2.



1. 4417-5486-1785-6411



NOTE: check digit is last digit (=1)



Drop last digit (the check digit):

  4417-5486-1785-641



Reverse digits:

  146-5871-6845-7144



Multiply odd-positions by 2:

  24(12)-5(16)72-6(16)4(10)-7248



Re-write mod-9:

  243-5772-6741-7248



Add all digits:

  2+4+3+5+7+7+2+6+7+4+1+7+2+4+8 = 69



Find the number that sums with 69 to make a multiple of 10:  1+69=70, 1 matches the check number.  EDIT (added this): Or, perhaps better, take the check digit (1) add to the above sum (69) to get 70, then check 70 mod 10.  If 0 then the credit card number is valid.







The number IS VALID.



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