Baruch MFE Spring 2012 Baruch MFE Facebook Contest

[dstefan]

All solutions are essentially the same - we gave 3 points to the fastest solution this time.

Three point answer:

Li Zhou
3 different states we could be in. We could be the farthest from the opposite (full diagonal) -> call this A, we could be on same face as the opposite point but not adjacent -> call this B, or we could be on the same face and adjacent -> call this C. I'm going to define E(A) as the expected number of steps from A to the opposite point. E(B) as the expected steps from B to the opposite, etc... So E(A) = 1 + E(B). E(B) = 1 + 1/3 E(A) + 2/3 E(C). E(C) = 1 + 2/3 E(B). 3 equations and 3 unknowns. Solve E(A) = 10

 

[dstefan]

Question 4 scores:

Li Zhou 3
Luis Toro 2
Lily Xiang 2
Dieter Dijkstra 2
Jin Kong 2
Nan Li 2
Yongyi Ye 2
Tuan Le 2
Gautam Punukollu 2
Babinu Uthup 1
Juan Pablo Alonso 1
Anthony Chi Wa Iao 1
Long Zhao 1
Raghuram Reddy 1
Trent Kilpatrick 1
Leo Yang 1
Balaji Nagarajan 1
Jeremia Msofu 0
Prashant Kumar 0

 

[dstefan]

Overall Standings:

Li Zhou 9
Luis Toro 9
Lily Xiang 8
Dieter Dijkstra 7
Jin Kong 7
Nan Li 7
Yongyi Ye 7
Babinu Uthup 6
Tuan Le 5
Juan Pablo Alonso 5
Anthony Chi Wa Iao 5
Gautam Punukollu 4
Long Zhao 4
Francesc Rosell Sanz 3
Raghuram Reddy 3
Trent Kilpatrick 3
Prashant Kumar 3

 

[dstefan]

In case of a points tie, there is only one tiebreaker: if someone has more 3 point answers than someone else, it will rank higher. Else, a tie for that spot will be declared.

Good luck, everyone!

 

[dstefan]

Question 5:

At the stockholder meeting, the board presented month-by-month profits/losses since the last meeting.
The CEO: ``We made profit over every consecutive 8-month period!"
A shareholder: ``Yeah, but you also lost money over every consecutive 5-month period!"
What is the maximum number of months that could have passed since the last meeting?

 

[dstefan]

Three point answer:

Amit Gupta
a1 + a2 ..... a5 < 0 ; a2+ a3+..... a6 <0 ... up to a8+a9.+ ...+a12 <0
As sum of every row is less than zero but sum of every column is > 0 which is not possible.
Hence 12 months are not possible, and a possible sequence for 11 months is
1,-1.6,1,1,-1.6,1,-1.6,1,1,-1.6,1

 

[dstefan]

Question 5 scores:

Amit Gupta 3
Yongyi Ye 2
Leo Yang 2
Nan Li 1
Alireza Kashef 1
Gerges Abdelsaid 1

 

[dstefan]

Overall Standings:

Yongyi Ye 9
Li Zhou 9
Luis Toro 9
Nan Li 8
Lily Xiang 8
Dieter Dijkstra 7
Jin Kong 7
Babinu Uthup 6
Amit Gupta 5
Tuan Le 5
Juan Pablo Alonso 5
Anthony Chi Wa Iao 5
Gautam Punukollu 4
Long Zhao 4

 

[dstefan]

Question 6:

For each subset of {1, 2, 3, ..., 2012} arrange the numbers in increasing order and take the sum with alternating signs. For example, for the subset {3} we get 3. For {2, 5, 8} we get 2 - 5 + 8 = 5. Find the sum of all the resulting integers.

 

[dstefan]

Question 6 scores:

Nan Li 3
Tuan Le 3
Alireza Kashef 3
Yongyi Ye 1
Li Zhou 1
Luis Toro 1
Lily Xiang 1
Jin Kong 1
Babinu Uthup 1
Amit Gupta 1
Raghuram Reddy 1
Jeremia Msofu 1
Mark Wahl 1
Mohammed Abdallah Bokhary 1

 

[dstefan]

Best Question 6 solution:
Alireza Kashef
we have 2^2012 subsets, 1 is present in half of them and is always positive, so we have 2^2011 times +1. for the rest of the numbers the sum of + and - is always zero because we have, for example for 6: the number of positives is when we have even numbers of 1,2,3,4,5 present and the number of negatives is when we have odd numbers of 1,2,3,4,5 present so the even number is combination (1,5) + combination (3,5) + combination (5,5), which is equal to combination (0,5) + combination (2,5) + combination (4,5) so the half of the 5's have + sign and half have - sign so the total is zero for anything other than 1 (5 is just an example and it could be k in general)

 

[dstefan]

Final Standings:

Nan Li 11
Li Zhou** 10
Luis Toro* 10
Yongyi Ye 10
Lily Xiang 9
Tuan Le 8
Jin Kong 8
Dieter Dijkstra 7
Babinu Uthup 7
Amit Gupta 6
Alireza Kashef 5
Juan Pablo Alonso 5
Anthony Chi Wa Iao 5

**Li Zhou had two 3 point answers
*Luis Toro had one 3 point answer
The number of 3 point answers was the tiebreaker for deciding the top three places.

 

[dstefan]

2012 Baruch MFE Facebook Contest Winners:

First Prize: Nan Li
Second Prize: Li Zhou
Third Prize: Luis Toro

 

[dstefan]

CONGRATULATIONS to Nan Li, the winner of the 2012 Baruch MFE Facebook Contest!!!

Congratulations to Li Zhou and to Luis Toro, the second and third prize winners!

 

[dstefan]

The winners should contact us at baruch.mfe@gmail.com for information on receiving their prizes.
Congratulations again!

 

[Brad Warren]

Congratulations to the winners!

 

[dstefan]

Thank you, Brad, on behalf of the winners

Brad is the winner of the first Baruch MFE Facebook contest last year.

 

[inferno]

Anything planned for Spring 2013?

 

[Tianyu Li]

I also would like to see the contest held again this spring, although I have already bought the books and it is not easy to visit FB from China.:D It is an interesting way of branding Baruch MFE through the mainstream social network and attracting more perspective applicants.

 

[dstefan]

We are planning on running the Facebook contest in November 2013.