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Q 4. The Erdös number of E at the beginning of the conference was: -
(1) 2
(2) 5
(3) 6
(4) 7
(5) 8

Q 5. How many participants had the same Erdös number at the beginning of the conference?
(1) 2
(2) 3
(3) 4
(4) 5
(5) Cannot be determined

Methodology

This LR caselet is full of data and information. One must take care to go through the questions and understand them thoroughly. Let us summarize the important points of this caselet. For the sake of simplicity, let's use the notation EN for Erdös Number.

General Information

1. Only Paul Erdös has an EN of zero.
2. Any mathematician who has written a paper with Erdös has an EN of 1.
3. When a group of mathematicians co-author a paper, every mathematician except the one with the lowest EN gets an EN equal to the lowest EN in the group + 1.

Specific Information

4. Initially A had infinite EN and F has the lowest EN.
5. F co-authored a paper with A and C which reduced the average EN of the group to 3. No other combination of three members would have brought down the average to 3.
6. After this five members had the same EN and the remaining three ENs were distinct.
7. E co-authored a paper with F which reduced the group's average by 0.5.
8. No other paper was authored.

We need to solve the caselet completely in order to answer the questions.

For the sake of simplicity, let us refer to the ENs of the members by their names in small letters. For example, let us denote the EN of A as a.

a = Infinity

Since F has the lowest EN, after co-authoring the paper with F, the ENs of A and C would become f + 1 each.

Since this brings the average of the group to 3, it means that the total of all the ENs now is 24.

9. a + b + c + d + e + f + g + h = 24

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