- 20 Sep '06 16:13Got too much work on at the moment, so am having a break from RHP for at least the next few months.

Since this is the only forum I have really posted in I thought I'd say bye and leave you with a couple of (hard) puzzles!!

1) A knight starts at the corner of a chessboard, and at each time t = 1, 2, 3, 4, ... it moves once, with all possible moves equally likely. Let T be the first time the knight returns to its starting corner. What is the expected value of T?

2) A monkey is typing on a typewriter, with each letter A, B, C, ... , Z equally likely. How long before you expect to see the sequence ABRACADABRA?

Enjoy! - 20 Sep '06 18:16An ugly incomplete solution for question 1

I can solve it with a system of 64 equations in 64 variables, in some mathematical software. Basically we need to write a number in each square of the chessboard, such that at a1 we have 0, and at each other square the number is 1 more than the average of the numbers which are at a knight's-move distance. Then the solution is the number at b3 (or c2) plus 1. (I think) - 20 Sep '06 19:32

Good luck SPMars! I always enjoyed your posts and analyses. Take care! We'll work on these in the meantime.*Originally posted by SPMars***Got too much work on at the moment, so am having a break from RHP for at least the next few months.**

Since this is the only forum I have really posted in I thought I'd say bye and leave you with a couple of (hard) puzzles!!

1) A knight starts at the corner of a chessboard, and at each time t = 1, 2, 3, 4, ... it moves once, with all possible moves equall ...[text shortened]... ... , Z equally likely. How long before you expect to see the sequence ABRACADABRA?

Enjoy! - 23 Sep '06 02:38

2) 26^11 letters is how many I'd expect before that sequence occurred.*Originally posted by SPMars***Got too much work on at the moment, so am having a break from RHP for at least the next few months.**

Since this is the only forum I have really posted in I thought I'd say bye and leave you with a couple of (hard) puzzles!!

1) A knight starts at the corner of a chessboard, and at each time t = 1, 2, 3, 4, ... it moves once, with all possible moves equall ...[text shortened]... ... , Z equally likely. How long before you expect to see the sequence ABRACADABRA?

Enjoy!