Question 187214

let put x= number of rows or number of columns

The designer has total characters: x*x +24 = x^2 + 24
If he add 1 row and 1 column then total charcters would be if filled out:
  (x+1)(x+1)= x^2+2x+1 
total character he has plus 25 empty one ( need to be filled) will be x^2+2x+1
so we can establish the equation as follows:

x^2+24+25 = x^2+2x+1
       49 = 2x + 1
       48 =2x =======> x=24 rows or 24 columns

Therefore designer has 24*24 +24= 576+24= 600 characters.