SOLUTION: A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters are left out. When he

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Question 64580: A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters are left out. When he tries to add one more row and column, he finds that he has 25 too few characters. Find the number of characters used by the designer.
Answer by 303795(602) About Me  (Show Source):
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The first square has 24 characters left over and the second square has 25 too few characters. The difference between the two squares must be 49 (25 + 24) characters.
The second square has x^2 grid positions. The first square has (x-1)^2=x^2-2x+1 grid positions.
The difference between these is 2x-1 grid positions which equals 49
2x-1=49
2x=50
x=25
so the second square has 25 rows and columns with 25 too few characters ie 625-25=600
The first square had 24 rows and columns with 24 too many characters ie 476+24=600