Problem 45389. Knight's Watch

Created by Asif Newaz

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[\"Night gathers, and now my watch begins\"]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>A knight is placed on an n-by-n sized chessboard at the position x. Find the probability that after k steps, the knight will remain within the chessboard.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Any knight's move that places him outside the board should be considered invalid.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ For simplicity, the knight's position on the chessboard is defined with the numeric\n notation instead of algebraic notation. so 'Ka1' is represented as (1,1).]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Brief explanation:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[Say the knight is placed in pos-(1,1). A knight has 8 possible moves. So in the next move, \nthe Knight can go to 8 different positions in the chessboard. But among them, only 2\npositions are valid i.e. the knight remains within the chessboard and they are -\n(3,2) & (2,3). So the prob. is 2/8 after 1 move. What will be the probability after k moves?]]></w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

16 Solutions
5 Solvers

Last Solution submitted on Apr 07, 2020

Last 200 Solutions

Problem Recent Solvers5

Problem Tags

algorithm chess probability

Problem 45389. Knight's Watch

Solution Stats

Last 200 Solutions

Problem Recent Solvers5

Suggested Problems

More from this Author148

Problem Tags

Problem 45389. Knight's Watch

Solution Stats

Last 200 Solutions

Problem Recent Solvers5

Suggested Problems

More from this Author148

Problem Tags

Players