There are 20! number of ways for everyone to do this so that at the end of the move, each seat is taken by exactly one person.
People are seated in a 2 by 10 rectangle grid. All 20 persons stand up from their seats and relocate to an orthogonally neighboring one upon the blowing of a whistle.
Now, we have to find the number of possible ways in which each seat is taken up by exactly one person after the move.
As the number of people is 20 and 20 seats are to filled exactly once.
So, the number of ways = 20!
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Using pythagorean theorem:
![\begin{gathered} c^2=a^2+b^2 \\ b=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{19^2-17^2} \\ b=\sqrt[]{72} \\ b\approx8.5 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20c%5E2%3Da%5E2%2Bb%5E2%20%5C%5C%20b%3D%5Csqrt%5B%5D%7Bc%5E2-a%5E2%7D%20%5C%5C%20b%3D%5Csqrt%5B%5D%7B19%5E2-17%5E2%7D%20%5C%5C%20b%3D%5Csqrt%5B%5D%7B72%7D%20%5C%5C%20b%5Capprox8.5%20%5Cend%7Bgathered%7D)
Substitute the values into the inequality:
-1 - 1 > 0
-2 > 0
False
