<p>Consider the paths of length <img alt="$16$" height="13" src="https://latex.artofproblemsolving.com/9/a/5/9a5b4928c8fe50ce3c2428da3bee3505e891b788.png" width="17" /> that follow the lines from the lower left corner to the upper right corner on an <img alt="$8\times 8$" height="12" src="https://latex.artofproblemsolving.com/1/9/7/1970593e80703dfe31ef799575bae2ee9819ced1.png" width="40" /> grid. Find the number of such paths that change direction exactly four times, as in the examples shown below.</p> <p><img alt="" src="/media/question/files/2024/11/22/q1-img.png" style="width: 458px; height: 217px;" /></p>

Question No: 226

Consider the paths of length $16$ that follow the lines from the lower left corner to the upper right corner on an $8\times 8$ grid. Find the number of such paths that change direction exactly four times, as in the examples shown below.

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Tags: Algebra Geometry

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