Find all integers a,b,c, and d satisfying:

1. 1<= a<=b<=c<=d
2. ab+cd = a+b+c+d+3

let

a=1+w

b=1+x

c=1+y

d=1+z

so we have,

(1+w+x+wx)+(1+y+z+yz) = 7+x+y+z+w

wx+yz = 5 . . . . . . . (i)

with the constraint    0<=w<=x<=y<=z  with  all  w , x , y , z belongs to integers

we have

wx + yz = 5+0

               = 4+1

               = 3+2

               = 2+3

               = 1+4

               = 0+5

ignoring first three cases on basis of constraint   0<=w<=x<=y<=z 

we have only 3 possible sets of solution,

w   x    y   z

1   1    2    2

1   1    1    4

0   0    1    5

=>    (a,b,c,d) = = (2,2,2,5) , (2,2,3,3) and (1,1,2,6)    are only possible solution

yes thats the right answer.........nice question