# Search results

1. ### Expected length of longest winning streak in a 162-game baseball season

Correct. However, as you know they're far from independent. If game 11 is a loss (50% chance) then there's no way for the set of games ranging from 2 to 11 to be the start of an 11-game streak. That dosen't sound like it will work. ACG
2. ### Expected length of longest winning streak in a 162-game baseball season

Hi! The Red Sox just finished an 11-game winning streak, which made me wonder. Do most teams experience winning streaks this long over the course of a season? What is the expected value of the length of the longest winning streak for a .500 team over the course of a season? In...
3. ### Traffic lane selection problem

Changing the time at which the driver leaves may not do much either. Remember that all of the other drivers are logical. If they all realize that the traffic at 8:30 jams up, they'll figure to go at different times. So they'll all go at 8:15 and the traffic will jam up at 8:15 instead :)...
4. ### Traffic lane selection problem

Hi! I've been dealing with a situation like this for a couple of years now and it made me start thinking... A city is populated entirely by infinitely logical drivers (I know, it's hypothetical :) . This city has two major N-lane highways (N > 1) which intersect each other at a...
5. ### Extension of Fermat's theorem?

Hi! That's cool -- I'd wondered about that myself :) However, that won't help here: the sum of four objects case would have to be a^5+b^5+c^5+d^5 = e^5. ACG
6. ### Extension of Fermat's theorem?

Hi! I assume you all know Fermat's last theorem. Well, has anyone considered the following extension to it? Assuming we're just using integers: We know that x1^n + x2^n = y^n has no solution for n > 2. However, what about this? For which values of k does x1^n+x2^n+...+xk^n = z^n...
7. ### Prime question

Hi! I was thinking about primes and have a bit of a question. I apologize if this is too easy or obvious -- I haven't thought much about it. Take two relatively prime numbers, P and Q. P < Q, and P is not prime. How many pairs (P,Q) are there so that ALL positive integers which are...
8. ### How many possible Sudoku boards are there?

Hi! I've got a couple of questions about Sudoku. 1. How many possible Sudoku boards are there? That is, a 3x3 square of 3x3 blocks where (a) each block has the numbers 1-9 exactly once, and (b) each row and column of the resulting 9x9 matrix has the numbers 1-9 exactly once? 2. I'm...