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

[Hunderpanzer]

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!

[MMcCarthy]

Since the job is over 2 months old, it's probably not still available anyway.

[Hunderpanzer]

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.

[MMcCarthy]

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.

[Banfa]

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.

[Hunderpanzer]

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.