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Suppose a classroom has 25 students seated in desks in a square 5 X 5 array. The teacher wants to al
seating by having every student move to an adjacent seat (just ahead, just behind, on the left, on the right). Show that such a move is impossible.
1 Answers
consider the 5 x 5 square of a chess board (black and white checked)
any horizontal or vertical move will simply change the colour of that child i.e. a child on a white desk must move to a black desk and vice versa.
the problem exists that in this 5 x 5 grid, there are 12 black desks and 13 white desks.
If every person at a white desk moved to a black desk there would be 1 child who would still have to sit at a white desk therefore this re-arragement is not possible
any horizontal or vertical move will simply change the colour of that child i.e. a child on a white desk must move to a black desk and vice versa.
the problem exists that in this 5 x 5 grid, there are 12 black desks and 13 white desks.
If every person at a white desk moved to a black desk there would be 1 child who would still have to sit at a white desk therefore this re-arragement is not possible
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