202 views

0 votes

Answer the question on the basis of the information given below:

Mathematicians are assigned a number called Zohos number (named after the famous mathematician, Paul Zohos). Only Paul Zohos himself has an Zohos number of zero. Any mathematician who has written a research paper with Zohos has an Zohos number of $1$. For other mathematicians, the calculation of his/her Zohos number is illustrated below:

Suppose that a mathematician $\text{X}$ has co-authored papers with several other mathematicians. From among them, mathematician $\text{Y}$ has the smallest Zohos number. Let the Zohos number of $\text{Y}$ be $y$. Then $\text{X}$ has an Zohos number of $y+1$. Hence any mathematician with no co-authorship chain connected to Zohos has an Zohos number of infinity.

In a seven day long mini-conference organized in memory of Paul Zohos, a close group of eight mathematicians, call them $\text{A, B, C, D, E, F, G and H}$, discussed some research problems. At the beginning of conference, $\text{A}$ was the only participant who had an infinite Zohos number. Nobody had an Zohos number less than that of $\text{F}$.

- On the third day of the conference $\text{F}$ co-authored a paper jointly with $\text{A}$ and $\text{C}$. This reduced the average Zohos number of the group of eight mathematicians to $3$. The Zohos numbers of $\text{B, D, E, G and H}$ remained unchanged with the writing of this paper. Further, no other co-authorship among any three members would have reduced the average Zohos number of the group of eight to as low as $3$.
- At the end of the third day, five members of this group had identical Zohos numbers while the other three had Zohos numbers distinct from each other.
- On the fifth day, $\text{E}$ co-authored a paper with $\text{F}$ which reduced the group’s average Zohos number by $0.5$. The Zohos numbers of the remaining six were unchanged with the writing of this paper.
- No other paper was written during the conference.

The Zohos number of $\text{C}$ at the end of the conference was: ________