Erdos Number puzzle--CAT'06, Demystifying the Myth

[studboy]

Hi All,
Most of you must have seen the Erdos number puzzle in CAT'06. All of the MBA prep Institutes and books are claiming that to be toughest.
Here is the solution which tries to prove the contrary, that it was the easiest puzzle. As the space is limited, only the solution is copied. Enjoy...You can get much more in the second edition of the book, CRACK the CAT published by Asian's and written by Vivek Gupta and Sandeep Amar.

Here it goes
On third day, F co authored a paper with A and C that reduced the average Erdos number to 3. Now, as F has the least Erdos number, it has to be 1 or 2. The reason is If F is 3, then everybody else would have 4 or more and that way’s the average can never be 3. As no other combination would have reduced the average to as low as 3, then C also should be highest among rest. (A was of course infinity)
Now, based on second statement, If F is 2, then A and C would be 3 along with three others from B,D,E,G and H. The other two would have erdos number >3 and has to be distinct. Even if they have 4 and 5, the average would not be 3 but greater than 3. So, F has to be 1. Hence, A and C after third day are 2 along with three from B,D,E,G and H.
Again, as the average is 3 which means a total of 24. So, F+A+C+Three from B,D,E,G and H are 1+2+2+2+2+2=11. So the rest two’s sum would be 13.
On the fifth day, E co-authored a paper with F which reduced the group’s average Erdos number by 0.5 So, E’s erdos number must have fallen by 4 and new erdos number of E would be 2. So E’s Initial erdos number was 6.
From above Para, as E is 6 one from B,D,G and H would be 7.
and we can also conclude, C would have more than 7 as from first statement, The combination of F, A and C would reduce the erdos number to maximum.
So, we can summarize the information as
F, initial=1 F, Final=1
A, initial=infinity A, final=2
C,initial (>7) C, Final=2
E, initial=6 E,final=2
B,D,G and H (Not in the order)
initial (2,2,2,7) final(2,2,2,7)


You can now mark all the solutions correctly.

[Oxymoron]

@studboy: Consider yourself warned...another instance of pseudo advertising out you go...

We do appreciate the effort in giving the solution for this problem but would have appreciated more if it had no ulterior motives.