Ekta Seth from India has managed to find the solution to this problem:

Total no. of black tiles required is 106. Reason:

• 315 =21x15
• Diagonal of the square= 6x sq.root of 2. So each side must be greater than 9.
• Since area of the rec.is 315, so length and breadth have to be integers.
• Thus border of the rec. has 68 tiles.
• Inside pattern require 38 tiles.
• Total=106 tiles.