# Is there a way to determine how many solution does “ The hundred Fowls problems” have looking at the coefficients?

I was looking at the different versions of the hundred fowls problems. I came across the problem posed by Chinese mathematicians posed in 5th century,and then Indians in 9th, 10th centuries. Alcuin of York also worked on this problem in 9th century. I can see the problem in Al-Khasi ' A key to Arithmetic' in 14th ( I guess) century. Many other mathematicians worked on this problems like Euler, Fibonacci and Simpson. Some of them offer the solutions for the problem some of them do not. I can follow the algebraic solution given by Simpson and Euler but it is really hard to follow the solution given by Al- Kashi and Fibonacci.

I was wondering if somebody know if there is a way to determine the number of solutions for any given version of 'The Hundred Fowls Problem" depending on the coefficients or using some other way. Since the solution need to whole number, many of the example given in the sources have one, two and a few number of solution, but I am very interested to know if we can tell possible number of solutions in different versions of The Hundred Fowls Problem?

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Hard to give a useful general answer. For many variants, one can produce a general parametric solution. – André Nicolas Dec 29 '12 at 16:50
@Andre Nicolas, what kind of parametric solution, can you be more specific please! – Deepak Dec 30 '12 at 4:11