Challenge "Fastest in the West"  

  By: admin on June 12, 2018, 1:24 p.m.

Buying a train ticket via credit card should not be a problem ā€” actually. Can you solve the subset-sum problem to get your train?

Re: Challenge  

  By: ExAstris on June 13, 2018, 3:04 a.m.


I understand (I think) how to get c from N. After finding c, since n/10=8, we get 8 bits.
What I don't understand is how (which system/method) is the credit card number (CC#) 22****65 encrypted to get c?
I read again about the knapsack problem, which I knew, and the subset-sum problem, which I didn't know, but I still don't see how the CC# is encrypted to yield c.

Any hints on the method ?

Thanks in advance!

Re: Challenge  

  By: AnLeRo on June 14, 2018, 8:27 p.m.


I'll try to describe the problem: you are given an array with 80 values and you are looking for the 8 values that sum up to c. Each value is at a certain position in the array and the concatenation of the 8 positions is the credit card number.

I hope this helps,

Re: Challenge  

  By: ExAstris on June 14, 2018, 10:42 p.m.

Thank you Anna,

it is very helpful, as I was trying to use the binary number instead of the positions.

I appreciate your support!

Re: Challenge  

  By: ExAmateur on June 19, 2018, midnight

I don't figure it out how to get c from N. Can you give me a hint for this challenge?
Thanks in advance.

Re: Challenge  

  By: ExAstris on June 21, 2018, 2:07 a.m.

I have not solved it, so don't take my word for it!

N has 80 numbers, you must find 8 numbers out of the 80 that will sum up to c. The concatenation of the positions of these 8 numbers ( I am assuming they are all 2-digit numbers) will provide the 16-digit credit card number (AnReLo explained this). However, I don't know how to find the correct ORDER of these 8 numbers.

Short example (those would be nice in the challenges' PDF):
Suppose n = 4 (the vector/array N contains 4 integers),
N=[1, 2, 4, 8], and c = 7. The only solution is
c = N[0] + N[1] + N[2] = 7. The positions are 00, 01, 02. So a 6-digit card number would be 000102. 010002, or 020001, could be a solution if the order didn't matter.

Hopefully, this is a little clearer.


Re: Challenge  

  By: AnLeRo on June 21, 2018, 2:31 p.m.

As you are given the first two and the last two digits of the credit card number, it might become obvious how to sort the positions as soon as you find the 8 values that sum up to cā€¦

Re: Challenge  

  By: ExAstris on June 21, 2018, 3:11 p.m.

Yes, without additional knowledge, there is an obvious order to try.
In my previous note, positions were starting at zero (as in my program), but they are probably counted from one.

Thank you Anna.


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