Question 58632
Let the 1st arrangement be x rows by x columns.
With 24 extra characters he must have x^2+24 characters.
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If he adds one row and one column his arrangement is 
(x+1)by (x+1) and he is 25 characters short so 
he has (x+1)^2-25 or x^2+2x-24 characters.
EQUATION:
x^2+24 = x^2+2x-24
2x=48
x=24
The number of characters he has is x^2+24
=24^2+24=24(25)=600
Cheers,
Stan H.