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

Question 27017: 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.
Um so yeah where in the world do i begin with this? I've been racking my brain and can't seem to get an answer...HELP!
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
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.
LET US START ASSUMING HE STARTED WITH N CROSS N GRID..
SO HE NEEDS N^2 CHARACTERS..
BUT HE WAS 24 CHARATERS SHORT..
THAT IS HE HAS N^2+24 CHARACTERS.
NOW HE TRIES (N+1) BY (N+1) GRID..
SO HE HAS (N+1)^2 SPACES..
HE HAS 25 FEWER.SO THE NUMBER OF CHARACTERS ARE (N+1)^2-25...HENCE...
N^2+24=(N+1)^2-25
(N+1)^2-N^2=24+25=49
N^+2N+1-N^2=49
2N=48
N=24
HENCE NUMBER OF CHARACTERS ARE
N^2+24=24^2+24=600

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