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# This problem may take some time...and programming.

 P: 60 I was just looking around on this site, and went into the Jobs category. I clicked on an interesting job advertisement for BitTorrent - I'm sure we all know what that is, and as a test, the employer wanted someone to give the answer to a problem which would prove their understanding of their math (maybe not so much) and python programming skills. Don't worry, I'm not looking to steal the answer and take the job. I know nothing of Python, but perhaps it can be done in another language ? Here it is. Let's see some results, and maybe some code used ? What is the exponent of the largest power of two whose base seven representation doesn't contain three zeros in a row? Good Luck! Jul 23 '07 #1
5 Replies

 Expert Mod 10K+ P: 14,534 Since the job is over 2 months old, it's probably not still available anyway. Jul 23 '07 #2

 P: 60 Since the job is over 2 months old, it's probably not still available anyway. True, but I've seen some pretty interesting math puzzles in this area of the forum, so I thought it would be cool to share it. Jul 23 '07 #3

 Expert Mod 10K+ P: 14,534 True, but I've seen some pretty interesting math puzzles in this area of the forum, so I thought it would be cool to share it. True, we do have some maths geniuses around. Jul 23 '07 #4

 Expert Mod 5K+ P: 8,962 What is the exponent of the largest power of two whose base seven representation doesn't contain three zeros in a row? Not as easy as it sounds, Python probably unqiuely suited to this problem, this is because most programming languages have a mimited set of integer types, for instance C/C++ typically has 8 bit integers 16 bit integers 32 bit integers 64 bit integers If you need anything else this needs to be programmed around. This is true for most languages, they have a set of limited integers, however Python has 2 types of integer 32 bit any size you want The second type clearly gives a very large problem domain, if you look at the base 7 representations of the first 31 powers of 2 (numbers fitting into a signed 32 bit int) none of them have 3 consecutive zeros. The first question has to be Are there any powers of 2 which have 3 consecutive 0s in their base 7 representation?Assuming the answer to that is yes the question then makes an assumption: At some value N the base severn representation of 2 ** x for all x >= N contains at least 3 consecutive 0s.This statement is not self evidently true to me however assuming that it is true then you need to find the minimum value of N and then the answer will be N-1. Personally I would say thorum solving like this involves mainly maths with little need for programming. In fact I think it would be very hard to write a program to some this to be true, you need to some something to be true for all x >= N not something a computer is very good at doing. Computers are good at doing something for all MIN_LIMIT <= x <= MAX_LIMIT but for this problem there is no max limit, a mathematical proof is required. Jul 23 '07 #5

 P: 60 Not as easy as it sounds, Python probably unqiuely suited to this problem, this is because most programming languages have a mimited set of integer types, for instance C/C++ typically has 8 bit integers 16 bit integers 32 bit integers 64 bit integers If you need anything else this needs to be programmed around. This is true for most languages, they have a set of limited integers, however Python has 2 types of integer 32 bit any size you want The second type clearly gives a very large problem domain, if you look at the base 7 representations of the first 31 powers of 2 (numbers fitting into a signed 32 bit int) none of them have 3 consecutive zeros. The first question has to be Are there any powers of 2 which have 3 consecutive 0s in their base 7 representation?Assuming the answer to that is yes the question then makes an assumption: At some value N the base severn representation of 2 ** x for all x >= N contains at least 3 consecutive 0s.This statement is not self evidently true to me however assuming that it is true then you need to find the minimum value of N and then the answer will be N-1. Personally I would say thorum solving like this involves mainly maths with little need for programming. In fact I think it would be very hard to write a program to some this to be true, you need to some something to be true for all x >= N not something a computer is very good at doing. Computers are good at doing something for all MIN_LIMIT <= x <= MAX_LIMIT but for this problem there is no max limit, a mathematical proof is required. I see. Maybe it's not such a great puzzle then. I'll keep an eye out for others. Jul 23 '07 #6 