DI Mathematics Puzzle
 

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

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

• In a seven day long mini-conference organized in memory of Paul Erdös, a close group of eight mathematicians, call them A, B, C, D, E, F, G and H, discussed some research problems. At the beginning of the conference, A was the only participant who had an infinite Erdös number. Nobody had an Erdös number less than that of F.
• On the third day of the conference F co-authored a paper jointly with A and C. This reduced the average Erdös number of the group of eight mathematicians to 3. The Erdös numbers of 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 Erdös 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 Erdös numbers while the other three had Erdös numbers distinct from each other.
• On the fifth day, E co-authored a paper with F which reduced the group‘s average Erdös number by 0.5. The Erdös numbers of the remaining six were unchanged with the writing of this paper.
• No other paper was written during the conference.

Q.1. The person having the largest Erdös number at the end of the conference must have had Erdös number (at that time):
1. 5
2. 7
3. 9
4. 14
5. 15

Q.2. How many participants in the conference did not change their Erdös number during the conference?
1. 2
2. 3
3. 4
4. 5
5. Cannot be determined

Q.3. The Erdös number of C at the end of the conference was:
1. 1
2. 2
3. 3
4. 4
5. 5

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

Answers Given Below (Select the area with mouse to see the answers)
1. 2
2. 4
3. 2
4. 3
5. 2