Puzzles

The common factors of 175 and 400 are 1, 5, 25. Hence in front and behind him there are either:

Therefore the shape of the formation is either 716×1, 126×5, or 24×25.

The length of the columns (716, 126, or 24) must be a factor of 312 and 264. Therefore it is 24.

Evariste is standing in the 8th row from the front and the 14th column from the left.

Evariste is standing in a rectangular formation, in which everyone is lined up in rows and columns. There are \(a\) people in all the rows in front of Evariste and \(b\) in the rows behind him. There are \(c\) in the columns to his left and \(d\) in the columns to his right.

For which numbers \(a\), \(b\), \(c\) and \(d\) is the row and column in which Evariste standing uniquely determined?