SOLUTION: a class of 25 students is arranged in 5 rows and 5 columns. If a student can move to a dest directly in front, behind, or to the left or right of their own desk, is it possiblefor

Question 29319: a class of 25 students is arranged in 5 rows and 5 columns. If a student can move to a dest directly in front, behind, or to the left or right of their own desk, is it possiblefor all the students to change desks at once and occupy a new desk?
Answer by bmauger(101) (Show Source): You can put this solution on YOUR website!
Nope. Prove this by using a checkerboard and placing 25 pieces on the board in a square. Now realize that by moving horizontal every piece must move to a different color than what they're on. How ever 13 will start on red squares and 12 on black (or vice-versa). So one red squared piece wouldn't be able to move to a black square, no matter how you arrange them.
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