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? -空指針異常- ♂ (0 bytes) () 03/30/2010 postreply 17:07:38

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

• 回複：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類似 -空指針異常- ♂ (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

• 檢查一下你的推導：p(1,1)=1/6p(2,3)+1/6p(3,2), p(2,3)=1/4 -空指針異常- ♂ (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

• 回複：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

• 另一種解法 -空指針異常- ♂ (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 -空指針異常- ♂ (0 bytes) () 03/31/2010 postreply 01:49:02