Prashanth,
Your question (slightly rephrased)
if you arrange N eggs in pairs one is left over
if you arrange N eggs in groups of three, two are left over
if you arrange N eggs in groups of four, three are left over
and so on, until
if you arrange N eggs in groups of nine, eight are left over
How many eggs?
Two approaches:
(1) Start with a simpler version and build up.
If you arrange N eggs in pairs one is left over.
Find the first several solutions (there are obviously many!)
If you arrange N eggs in pairs one is left over
If you arrange N eggs in groups of three, two are left over
Find the first several solutions
Now use three rules; look for a pattern; extend it.

(2) Change the problem. Suppose you had one more egg...
Good Hunting!
RD
