<PRE><B>Question 1201865</B>
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The figure is described as a 7x22 grid of unit squares, so we don&#39;t need to see the figure....&lt;br&gt;
Assuming this is a problem where A and B are opposite corners of the grid, the number of paths of length 29 from A to B is&lt;br&gt;
{{{29!/((22!)(7!))}}}&lt;br&gt;
To understand the reason for that answer, let B be 22 units to the right of A and 7 units above A.  Then any path from A to B of length 29 has to move 22 &quot;steps&quot; to the right (&quot;R&quot;) and 7 steps up (&quot;U&quot;).&lt;br&gt;
So each path of length 29 from A to B consists of some arrangement of the symbols&lt;br&gt;
RRRRRRRRRRRRRRRRRRRRRRUUUUUUU&lt;br&gt;
By a well-known counting principle, the number of ways to do that is the number shown above.&lt;br&gt;
ANSWER: {{{29!/((22!)(7!))}}}&lt;br&gt;
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