Maybe we should use some algebra in there somewhere instead
of using trial and error.

Normally we would expect that if the sum of the 4 people's
ages is now 68, then four years ago each would have been 4 
years younger, and the sum would have been 4*4 or 16 less.
But 16 less than 68 is 52, not 53. 

So the youngest child must not have been born 4 years ago.

So 4 years ago there were only 3 members of the family

Let the sum of the ages of the 3 older members of the family be x.
Let the age of the youngest child who wasn't born 4 years ago be y.

Then x + y = 68 and since 4 years ago there were only 3 members of
the family the sum would have been only 4*3 or 12 less. So

x-12 = 53
x = 65

And since x + y = 68, substituting x = 65
         65 + y = 68
              y = 3

The youngest child is 3.

Edwin