Problem 2405. The Number of Ways

Created by Abdullah Caliskan

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=\"text\"/></w:pPr><w:r><w:t>Find all the possible ways to reach the end of a matrix. So given</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[[a b\n c d]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>the possible ways [a c],[a d],[b c],[b d] as inputs</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>p</w:t></w:r><w:r><w:t> the number of rows and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>n</w:t></w:r><w:r><w:t> the number of column. You will produce a matrix by using these two input inputs. The matrix starts with 1 and increases left to right. The last number in the matrix will be n*p. After that you find the possible ways to reach end of the matrix</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example 1</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[p = 2; the number of rows \nn = 2; the number of columns\n\nwill produce this output matrix \n\n[1 2 \n 3 4]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Possible ways are [1 3],[1 4],[2 3],[2 4]</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ output =\n\n 1 3\n 1 4\n 2 3\n 2 4]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example 2</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ p = 4;\n n = 2;]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>These produce the matrix</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ [1 2\n 3 4\n 5 6\n 7 8]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Possible ways are [1 3 5 7], [1 3 5 8],...,[2 4 6 8]</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ output =\n 1 3 5 7\n 1 3 5 8\n 1 3 6 7\n 1 3 6 8\n 1 4 5 7\n 1 4 5 8\n 1 4 6 7\n 1 4 6 8\n 2 3 5 7\n 2 3 5 8\n 2 3 6 7\n 2 3 6 8\n 2 4 5 7\n 2 4 5 8\n 2 4 6 7\n 2 4 6 8]]></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>"}]}

Find all the possible ways to reach the end of a matrix. So given<pre class="language-matlab">[a b
 c d] 
</pre>the possible ways [a c],[a d],[b c],[b d] as inputs p the number of rows and n the number of column. You will produce a matrix by using these two input inputs. The matrix starts with 1 and increases left to right. The last number in the matrix will be n*p. After that you find the possible ways to reach end of the matrixExample 1<pre class="language-matlab">p = 2; the number of rows 
n = 2; the number of columns
</pre><pre class="language-matlab">will produce this output matrix 
</pre><pre class="language-matlab">[1 2 
 3 4]
</pre>Possible ways are [1 3],[1 4],[2 3],[2 4]<pre> output =</pre><pre> 1 3
 1 4
 2 3
 2 4</pre>Example 2<pre> p = 4;
 n = 2;</pre>These produce the matrix<pre> [1 2
 3 4
 5 6
 7 8]</pre>Possible ways are [1 3 5 7], [1 3 5 8],...,[2 4 6 8]<pre> output =
 1 3 5 7
 1 3 5 8
 1 3 6 7
 1 3 6 8
 1 4 5 7
 1 4 5 8
 1 4 6 7
 1 4 6 8
 2 3 5 7
 2 3 5 8
 2 3 6 7
 2 3 6 8
 2 4 5 7
 2 4 5 8
 2 4 6 7
 2 4 6 8</pre>

Find all the possible ways to reach the end of a matrix. So given

[a b
   c d]

the possible ways [a c],[a d],[b c],[b d] as inputs *p* the number of rows and *n* the number of column. You will produce a matrix by using these two input inputs. The matrix starts with 1 and increases left to right. The last number in the matrix will be n*p. After that you find the possible ways to reach end of the matrix

Example 1

p = 2; the number of rows 
  n = 2; the number of columns

will produce this output matrix

[1 2 
   3 4]

Possible ways are [1 3],[1 4],[2 3],[2 4]
  
 output =

1     3
     1     4
     2     3
     2     4

Example 2

p = 4;
 n = 2;

These produce the matrix

[1 2
  3 4
  5 6
  7 8]

Possible ways are [1 3 5 7], [1 3 5 8],...,[2 4 6 8]

output =
     1     3     5     7
     1     3     5     8
     1     3     6     7
     1     3     6     8
     1     4     5     7
     1     4     5     8
     1     4     6     7
     1     4     6     8
     2     3     5     7
     2     3     5     8
     2     3     6     7
     2     3     6     8
     2     4     5     7
     2     4     5     8
     2     4     6     7
     2     4     6     8

Solve

Solution Stats

34 Solutions
19 Solvers

Last Solution submitted on Jun 30, 2021

Last 200 Solutions

Problem Comments

Solution Comments

Solution 468023

2 Comments

2 Comments

Jan Orwat on 9 Jul 2014

It won't work correctly for n greater than 10. :-)
ans-7*(ans>10) would fix that.

Alfonso Nieto-Castanon on 9 Jul 2014

You are right, you could use ind2sub to avoid some of the limitations of dec2base as well (e.g. for n>36)...

Problem Recent Solvers19

Problem Tags

matrix manipulation

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 2405. The Number of Ways

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers19

Suggested Problems

More from this Author21

Problem Tags

Community Treasure Hunt

Problem 2405. The Number of Ways

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers19

Suggested Problems

More from this Author21

Problem Tags

Community Treasure Hunt

Players