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35280, because credit card numbers do not start with ‘0’.
I’m rusty Neil and WJ, so tell me what I’m doing wrong. We can repeat numbers, so isn’t the logic:
7 ways to choose 1st number * 8 ways to choose 2nd * 8 ways to choose 3rd * … * 8 ways to chose 8th number = 14,680,064
The first digit of a creditcard has significance as to for what it was issued. We can make assumptions as far as whether he uses American Express (first digit is a 3) or if he uses Visa or MasterCard (a 4 or 5), Discover (first digit a 6). He could be screwin with us though and may be referring to a Gas card or Airline card of his, which could have a 7 or 1 respectively. Officially however, cards are able to start with a 0, but you would have little to no reason of ever seeing one of those.
Another difficulty is that not all cards are 16 digits long. They vary depending on the company and can be nearly anything from 12 to 19 digits long. (american express cards are always 15 digits, while visa can be 13 or 16, discover is always 16…) Again, we can reduce our number of total possibilities if we make assumptions, but perhaps he has a swiss bank account card..
I might work on the problem a bit more after returning home from work, but the problem is much more difficult than you have thought so far.
(of course ignoring the easy way out and assuming each time we guess, we guess a different number than any of the previous guesses. if we are allowed to guess the same number over and over, it is able to be endless)
Working from http://en.wikipedia.org/wiki/Bank_card_number
Assuming it’s a major brand, it can only be mastercard or discover, since Visa cards start with 4 and AmEx numbers are 15 digits. The possibilities are
52xx xxxx 6812 7167
53xx xxxx 6812 7167
65xx xxxx 6812 7167
Skipping the question of the minimum possible guesses and brute forcing it with python/sage, the only possiblities with valid check digits are the 144 listed here: http://pastebin.com/0Yq8RQ8L
Another dubious assumption is that stealing Daniel’s credit will somehow lead to the “good life.” Could be a trick question entirely — if you can do the math, you are already living the good life.
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