Question

There are 25 seats in a certain classroom, arranged in five rows of five seats per row. Each student is to change seats by going to one of the four nearest seats -- the seat directly behind, directly in front, immediately to the left or immediately to the right of the seat he or she is currently using. Sitting on the floor isn't an option -- and neither is sitting in someone's lap! Determine whether a rearrangement following these rules is possible, starting with a full class of 25 students, and explain your answer.

Answer 1

i think it is not possible

Answer 2

I dont think its possible. Lets say you colored the desks like a chess board, alternating colors. Then there would be either more white than black, or vice versa (since there are 25 seats). Every kid that moves would end up in a color opposite the one they had. but if you are in a desk whose color there is more of, there arent enough of the opposite color for you.

Answer 3

like if there were more black desks than white, when everyone switches there arent enough white desks to accommodate them.

Answer 4

i think the question means that the students are to move simultaneously, so when one student is rising up to move on to another seat (which will now be vacant because the student who sat there awhile ago has also risen), another student will occupy this seat. So since the number of seats equal the number of students, there will be enough seats for everyone. The question is, can this be done when the students are only allowed to switch to a seat directly in front, behind, left, or right of him.

Answer 5

its not possible, try a few simulations on paper, you will always end up with one kid not being able to move.

Answer 6

its not like they can move across the room, they can only move up down left and right. That restriction is what makes it not possible.

Answer 7

Think of the desks like this picture. if i kid is in a white seat, no matter how he moves he will end up in a black seat. theres no way to get around that. There are 13 black and 12 white seats. When everyone switches, there is no way for the 13 kids that were in black seats to find enough white seats. its impossible.