Problem 2405. The Number of Ways

Created by Abdullah Caliskan

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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

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Last Solution submitted on Aug 23, 2022

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Solution 468023

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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)...

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Problem 2405. The Number of Ways

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