SOLUTION: A tiled floor of a room has a dimension m*m sq-m dimensions of tile used are n*n sq-m. All tiles used are green tiles except diagonal tiles are red. After some years some green til

SOLUTION: A tiled floor of a room has a dimension mm sq-m dimensions of tile used are nn sq-m. All tiles used are green tiles except diagonal tiles are red. After some years some green til

Question 890619: A tiled floor of a room has a dimension m*m sq-m dimensions of tile used are n*n sq-m. All tiles used are green tiles except diagonal tiles are red. After some years some green tiles are replaced by red tiles to form alternate red and green tiles pattern how many green tiles are removed? (m not equal to n)
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If the floor is completely covered with the tiles, then is a positive integer.
That is the number of tiles along each side of the square room,
and it is also the number of tiles in the diagonal.
The total number of tiles is .

If is even, in an alternating pattern, half of the tiles would be red.
The final number of red tiles would be

The number of green tiles replaced (the number of red tiles added) would be

If is an odd number, an alternating pattern with a red diagonal would have
red tiles and green tiles.
The number of green tiles to be replaced (the number of red tiles to be added) would be

UNFORTUNATELY, there is no simple formula that covers both cases (when is even, and when is odd).
If you want a single formula, I would have to write something complicated, like
or

For , which is odd, we are replacing
tiles, or
tiles, or
tiles.
The new (replacement) red tiles are the ones in the green triangles.
There are in each triangle.
RELATED QUESTIONS
How many tiles are required to cover a floor of length 6 m and breadth 4 m if the area... (answered by Cromlix)

How many tiles are required to cover a floor of length 6 m and breadth 4 m if the area... (answered by fractalier)

Floor tiles are 15 cm squares.how many tiles will be needed for a floor measuring 12 m by (answered by DENNIS DON,ikleyn)

A room measuring 11 2/3 m by 7 7/8 m is to be tiled with square tiles of maximum size so... (answered by greenestamps)

a classroom is 10 yards long. the floor is being tiled with new sq. tiles that are each... (answered by josh_jordan)

Can someone please explain the problem If a room has a width of 5 m, a length of 6 m,... (answered by greenestamps)

Hi Can someone please help with question If a room has a width of 5 m, a length of 6... (answered by addingup,jim_thompson5910)

A rectangular floor in my office has its area equal to 56 m^2. The minimum number of... (answered by jim_thompson5910)

The minimum number of identical square tiles required to tile a large rectangular... (answered by Alan3354)