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/sci/ - Science & Math

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1626686 No.1626686 [Reply] [Original]

Ok /sci/

Seats are arranged in a classroom in five rows and seven columns, the instructor tells the students that they can move forwards backwards left or right one seat but not diagonally

1.) This is impossible Prove Why

2.) If diagonal movement were allowed why would it be possible

>> No.1626694

It's impossible to what?

>> No.1626698

to have every student me moved into a different seat

>> No.1626700

So you can swap them like in Bejeweled?

>> No.1626706

You never said how many students, only how many seats. So there are 2 students, and it's easily possible.

>> No.1626708

Yes, they can move one forward, backward, or left to right, the objective is to have each one in a new seat, without moving diagonally this is impossible, prove why, and if they could move diagonally explain why its possible

Just something we did today in CALC II that i thought was cool

>> No.1626711

Because you can not draw any combination of closed loops given those constraints

>> No.1626726
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1626726

>> No.1627514

>>1626726
Color the classroom like so. Then, a student in a white seat must move to a black seat and vice versa. Assuming it was possible, then every student must have changed seat, and so every student in a white seat must have moved to a black seat. However, there are 18 white seats, but 17 black seats, so it is impossible.

If we allow for diagonal movement, then students can move to seats of the same color they originally sat in, so the proof doesn't work, and finding a counterexample is fairly easy.