Mathematicians are assigned a number called the Elliot
number, named after the famous mathematician Paul Elliot.
Only Paul Elliot has an Elliot number 1, the lowest possible.
Any mathematician who has written a research paper with
Elliot has an Elliot number of 2. For other mathematicians,
the calculation of his/her Elliot number is as follows
Suppose that a mathematician X has co-authored
papers with several other mathematicians. From among
them, mathematician Y has the smallest Elliot number.
Let the Elliot number of Y be y. Then, X has an Elliot
number of y + 1 while that of Y would remain the same.
Hence, any mathematician with no co- authorship chain
connected to Elliot has an Elliot number of infinity.
Ten mathematicians – A, B, C, D, E, F, G, H, I and J -
had come for a four-day conference. Among the ten,
only C and G had written research papers with Elliot.
On the first day, C co-authored a paper with B and I,
which bought down the average Elliot number of the
group by the maximum possible value. Further, no
other co-authorship of C with any two other than B or I
would have reduced the average Elliot number of the
group by such a huge value. The Elliot number of the
other seven mathematicians remained unchanged and
now all the ten had single digit Elliot numbers.
On the second day, H co-authored a paper with E,
which reduced the average Elliot number of the group
by 0.5. After the co-authorship, the Elliot number of H
was less than E’s and no other co-authorship of H with
any other person in the group would have reduced the
average of the group by 0.5.
On the third day, B co-authored a paper with D and J,
This reduced the average Elliot number of the group to
3.4 from 4.1
On the fourth day, A co-authored a paper with F and there
was no change in the average Elliot number of the group
No other paper was written during the conference.
1. At the end of day 1, who had the highest Elliot
number among the ten mathematicians?
(A) A (B) D (C) E (D) J
2. Which of the following could have been the Elliot
number of A at the beginning of the conference?
(A) 3 (B) 4 (C) 6 (D) 8