NMOS 2010 Q4

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3 + 4 + 5 + 6 + 7 + 8 + 9 = 42 -- even number

So thee number in the box at the intersection will have to be an even number -- 4, 6 or 8.

42 + 4 = 46

46 / 2 = 23

4 + 6 + 5 + 8 = 23     4 + 3 + 7 + 9 =  23

Digit 4 is fixed, so only 1 way.

5, 6 and 8 --> 3 x 2 x 1 = 6 ways

3, 7 and 9 --> 3 x 2 x 1 = 6 ways

5, 6, 8 and 3, 7, 9 can be switched, i.e. vertical becomes horizontal and horizontal becomes vertical

So total number of ways --> 1 x 6 x 6 x 2 = 72


42 + 6 = 48

48/2 = 24

6 + 7 + 3 + 8 = 24,   6 + 4 + 5 + 9 = 24


Number of ways --> 72 ways
   
42 + 8 = 50

50 / 2 = 25

8 + 7 + 4 + 6 = 25,   8 + 3 + 5 + 9 = 25

Number of ways --> 72 ways



Total number of ways --> 72 x 3 = 216.