How to work out how many tiles cover the floor?

Question

A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor?

Puzzling · Accepted Answer

You have two diagonals. Since they cover an *odd* number of squares, there must be a center square that they share.
x + x - 1 = 37
2x - 1 = 37
2x = 38
x = 19

Summary:
In a 19 by 19 grid, you have 19 tiles on each diagonal, but one that is shared.
19 + 19 - 1 = 37 tiles

The total number of tiles in a 19 x 19 grid is:
19² = 361

Answer:
361

? · Answer

361 times your floor is 19 x 19. That gives you 37 tiles on the diagonal one tike overlaps both diagonal.

How to work out how many tiles cover the floor?

2 Answers