Challenge: Sets whose Elements Sum to...

[NotLKH]

Given:
	You have 13 variables, F_0 thru F_12, that represent 13 distinct sets of numbers.
	These Variables, The Number of elements in their sets, and the sums of the 
	elements in their sets are listed below:
		F(n)		#Elements		Sums(Of their elements)
		F(0)		#=1			Sum=0
		F(1)		#=6			Sum=22
		F(2)		#=3			Sum=50
		F(3)		#=3			Sum=41
		F(4)		#=6			Sum=58
		F(5)		#=6			Sum=147
		F(6)		#=6			Sum=156
		F(7)		#=6			Sum=203
		F(8)		#=3			Sum=177
		F(9)		#=3			Sum=168
		F(10)		#=6			Sum=295
		F(11)		#=6			Sum=286
		F(12)		#=6			Sum=227



	The sets can only use the numbers 0 thru 60, and cumulatively, these numbers
	are used once and only once across the entire sets of variables.

So for example,
	Consider:
		F(8)		#=3			Sum=177
	This identifies that:
		F(8) is the sum of 3 numbers that add to 177

	Since the range of all possible numbers that F(8) can draw from is 0->60 
	{or for that matter, Any of the F variable sets};
		And since the TOP(3) Values, 58,59,60 sum to 177
	We know that F(8) MUST BE {58,59,60}
		[if any of the distinct elements for F(8) were less than 58, 
		then it would require a number greater than 60 to also be 
		an element, which is beyond the allowed range.]
	And at this point we also know that the numbers 58 59 and 60
	Cannot be used by any other Variable set other than F(8), which simplifies
	the analysis of the remaining F sets.

Therefore:
	Either
		Determine the 2 possible sets of numbers for F(4)
	OR
		Tell me why F(4) has either more or less than 2 solution sets.

Enjoy!