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Well, let's see. There has to be a whole-number of players in each row and

each column (rank and file), so the dimensions ofthe rectangle have to be

the whole-number factors of 50.

So the only arrangements we see, without leaving any empty places, are

1 x 50

2 x 25

5 x 10

players.

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Q: How many different ways can 50 players in a marching band be arranged in rectangle arrangements?
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