A stockholder meeting

[radosr]

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

 

[anujjain]

Maximum Number of month is 11.
Proof: Sufficient to prove that 12 months are not possible.
Let an denote the P&l on the nth month.
Then we have
a1+a2+a3+a4+a5 <0
a2+..............<0
..
..
..
a8+a9+a10+a11+a12<0
Now sum of each row is less than zero but sum of every column is positive. Hence can't be true.
Possible sequence for 11 months is
1,-1.6,1,1,-1.6,1,-1.6,1,1,-1.6,1.

 

[pruse]

this is such a classic. it appeared at the IMO many years ago.

 

[pratikpoddar]

Very interesting problem. You can get the solution at http://pratikpoddarcse.blogspot.com/2010/07/differing-views.html
Cheers!

 

[euroazn]

Maximum Number of month is 11.
Proof: Sufficient to prove that 12 months are not possible.
Let an denote the P&l on the nth month.
Then we have
a1+a2+a3+a4+a5 <0
a2+..............<0
..
..
..
a8+a9+a10+a11+a12<0
Now sum of each row is less than zero but sum of every column is positive. Hence can't be true.
Possible sequence for 11 months is
1,-1.6,1,1,-1.6,1,-1.6,1,1,-1.6,1.

Elegant.