Each of x, y and z are positive integers such that x+y+z=2006 and, x!*y!*z! = p*10^{q}, where each of p and q is a positive integer and p is not divisible by 10.

What is the smallest value of q?

(In reply to

re(2): Paper and pencil solution (spoiler?) by broll)

**There are many other solutions (all getting 492), inter alia**

124 +1124
+758,123 +1124+759, 624+623+759 ,

1249 + 374
+383 ,1248+374+384 etc etc

I will adddres this puzzle later