@shashank:  your approach fails for (2,0,0,0) & (1,1,1,1)

but.. from any of the above approaches seen, we couldn't be 100% sure of 
the solution,
but, from shashank's approach, the probability of finding correct soultion 
can be improved by using some random prime numbers.
(running tests for more than one prime number)

and for any other approaches, a mathematical proof is needed to support the 
answer.

(better accuracy over time is the trade off in the seen examples)

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