Knight Jump

A knigh jumps aimlessly on an 5X5 empty ches*****oard. At each step, it chooses an admissible position with equal probability and jumps there.

(1) If the knight starts from the center, what is the probability that it will hit one of the corners before returning to the center?

(2)If the knights starts from a corner, what is the expected time for it to reach the center?

所有跟帖： 

• Q1: 1/12? -空指针异常- ♂ (0 bytes) () 03/30/2010 postreply 17:07:38

• oops, any one corner: 1/3; certain one corner: 1/12 -空指针异常- ♂ (0 bytes) () 03/31/2010 postreply 01:18:27

• 回复：oops, any one corner: 1/3; certain one corner: 1/12 -jinjing- ♀ (67 bytes) () 03/31/2010 postreply 10:51:09

• 思路跟sum of dice throwing类似 -空指针异常- ♂ (780 bytes) () 03/31/2010 postreply 11:29:23

• If p(1,1)=1/12,p(1,1)=1/6p(2,3)+1/6p(3,2),p(2,3)=1??? -jinjing- ♀ (184 bytes) () 03/31/2010 postreply 17:18:21

• 检查一下你的推导：p(1,1)=1/6p(2,3)+1/6p(3,2), p(2,3)=1/4 -空指针异常- ♂ (66 bytes) () 04/01/2010 postreply 12:25:40

• you should be know:4p(23)=1,as p(23)=p(32)=p(24)=p(43) -jinjing- ♀ (120 bytes) () 04/01/2010 postreply 14:53:52

• 回复：you should know:4p(23)=1,as p(23)=p(32)=p(24)=p(43) -jinjing- ♀ (0 bytes) () 04/01/2010 postreply 14:55:22

• 另一种解法 -空指针异常- ♂ (984 bytes) () 03/31/2010 postreply 11:55:02

• You use step method is good,but .... -jinjing- ♀ (172 bytes) () 04/01/2010 postreply 16:35:25

• 4 steps random move is 7/72, 1/12 is too small -jinjing- ♀ (44 bytes) () 03/30/2010 postreply 18:34:37

• Q2: 18 -空指针异常- ♂ (0 bytes) () 03/31/2010 postreply 01:49:02