Q. In a square shaped room, the floor is of black and white color tiles. There are a total of 81 black colored tiles along the diagonals are there and the remaining are white. What are the total no. of tiles in the room?

Option
A. 900
B. 1681
C. 1600
D. 2500

• no. of black tiles along the diagonals=81
  let n be the no. of square blocks in a row/column then
  no. of blocks along diagonals=(2*n-1)if odd no's of blocks are there
  (2*n-1)=81
  or 2n=82
  or n=41
  so,total no. of tiles in the room =n^2= 41^2=1681
  ans(b)
  
  
• 11 years agoHelpfull: Yes(49) No(2)
• The diagonal running from top left to bottom right will have one square in every column. So an n x n square will have n tiles in the diagonal.
  
  The same will be true for the other diagonal, but if the dimensions of the square are odd, the diagonals will have a common tile at the centre.
  
  n being even: Tiles in diagonal = 2n
  n being odd: Tiles in diagonal = 2n - 1 (which itself is odd)
  
  So if there are 81 tiles in the diagonal, n must be odd.
  Solving 2n minus 1 = 81 implies 2n = 82 implies n = 41.
  Hence, there are 41 times 41 = 1681 tiles in the room.
• 11 years agoHelpfull: Yes(6) No(1)
• c 1600
  resn
  number of rows or columns=(number of diagonal tiles+1)/2
  +1 because one tile is common in both the diagonals
  so number of rows = 82/2= 41
  now total tiles= 41*41= 1681
  white tiles = 1681-81=1600
• 11 years agoHelpfull: Yes(5) No(11)
• ans=1681
  number of rows or columns=(number of diagonal tiles+1)/2
  no.of rows=82/2=41
  so,total no of tiles=41*41=1681.
  
• 11 years agoHelpfull: Yes(4) No(1)
• 1681 is the correct answer.
• 11 years agoHelpfull: Yes(2) No(1)
• 1681 is total no of tiles
  
• 11 years agoHelpfull: Yes(2) No(2)
• which is the correct answer??
• 11 years agoHelpfull: Yes(0) No(1)