The word BRAIN

Puzzle Question:

Each of the five characters in the word BRAIN has a different value between 0 and 9. Using the given grid, can you find out the value of each character?
B R A I N 31
B B R B A 31
N I A B B 32
N I B A I 30
I R A A A 23
37 29 25 27 29
The numbers on the extreme right represent the sum of the values represented by the characters in that row. Also, the numbers on the last raw represent the sum of the values represented by the characters in that column. e.g. B + R + A + I + N = 31 (from first row)

Answer --

Solution of Puzzle:

B=7, R=6, A=4, I=5 and N=9
Make total 10 equations - 5 for rows and 5 for columns - and sovle them.
From Row3 and Row4,
N + I + A + B + B = N + I + B + A + I + 2
B = I + 2
From Row1 and Row3,
B + R + A + I + N = N + I + A + B + B - 1
R = B - 1
From Column2,
R + B + I + I + R = 29
B + 2R + 2I = 29
B + 2(B - 1) + 2I = 29
3B + 2I = 31
3(I + 2) + 2I = 31
5I = 25
I = 5
Hence, B=7 and R=6
From Row2,
B + B + R + B + A = 31
3B + R + A = 31
3(7) + 6 + A = 31
A = 4
From Row1,
B + R + A + I + N = 31
7 + 6 + 4 + 5 + N = 31
N = 9
Thus, B=7, R=6, A=4, I=5 and N=9

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