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   Author  Topic: How many Birds  (Read 12153 times)
Rivaa
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How many Birds  
« on: Dec 10th, 2012, 8:50pm »
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One bird is leading two birds, now tow birds are leading one bird... so how many birds are there.....?
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towr
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Re: How many Birds  
« Reply #1 on: Dec 10th, 2012, 10:40pm »
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3
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cartoonle
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Re: How many Birds  
« Reply #2 on: Dec 10th, 2012, 11:48pm »
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tow is two?
 
than 3 birds?
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Rivaa
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Re: How many Birds  
« Reply #3 on: Dec 11th, 2012, 5:13am »
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ya cartoonle the total no of birds are 3 Smiley
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marlonmark
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Re: How many Birds  
« Reply #4 on: Jan 2nd, 2013, 2:20am »
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answer will 3 my friend it was already said by Towr
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Re: How many Birds  
« Reply #5 on: Jan 28th, 2013, 10:00am »
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I thought it was two  Shocked
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Re: How many Birds  
« Reply #6 on: Feb 7th, 2013, 11:36am »
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If ans is 3 your question was right   Smiley
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Re: How many Birds  
« Reply #7 on: Feb 17th, 2013, 5:12am »
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3, of course!
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Re: How many Birds  
« Reply #8 on: Feb 20th, 2013, 4:13am »
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it's 3
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tsitut
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Re: How many Birds  
« Reply #9 on: Feb 20th, 2013, 12:11pm »
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3 obviously XD
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Re: How many Birds  
« Reply #10 on: Apr 6th, 2013, 11:39pm »
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only three
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whizen
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Re: How many Birds  
« Reply #11 on: May 29th, 2013, 6:04pm »
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Are the birds in the first part of the question the same ones as the birds in the second?
In that case, there are 6 birds... counting the bird that I have in my hand, and the 2 in the bush.
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Re: How many Birds  
« Reply #12 on: Aug 2nd, 2013, 7:58am »
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Did you see them birds?
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Re: How many Birds  
« Reply #13 on: Aug 24th, 2013, 11:19am »
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.<:>.
 
.=bird
 
So to me there are four 4 birds. One bird "towing" two birds and "the" two birds in "tow" are leading one bird. Since the one bird is not capitalized then it's name is not One Bird or "the" one bird...so there can be four. Most likely I am over thinking things again  Wink
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sanaya
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Re: How many Birds  
« Reply #14 on: Sep 2nd, 2013, 5:33am »
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3 birds...I am sure
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Re: How many Birds  
« Reply #15 on: Sep 17th, 2013, 1:21am »
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4 birds buddies
 
b1-b2,b3-b4
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aiyanct
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Re: How many Birds  
« Reply #16 on: Nov 29th, 2013, 11:12pm »
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ITS THREE  "3"
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OmerMustafa
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Re: How many Birds  
« Reply #17 on: Dec 14th, 2013, 3:47am »
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6 birds if the birds in the second part of the question are different with the birds of first part  Grin
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AKMBorhanice
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Re: How many Birds  
« Reply #18 on: Jan 20th, 2014, 12:26pm »
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Yes it is , 3 Birds
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progagan
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Re: How many Birds  
« Reply #19 on: Jan 23rd, 2014, 11:26pm »
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There are three birds. I am sure...
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Re: How many Birds  
« Reply #20 on: Jan 30th, 2014, 8:12pm »
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Five birds. Two birds ahead are leading one bird in the middle that is leading the last two birds.
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jordan
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Re: How many Birds  
« Reply #21 on: Feb 2nd, 2014, 1:04am »
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and what is the right answer? I didn't get it Smiley
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Re: How many Birds  
« Reply #22 on: Feb 10th, 2014, 8:26pm »
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I'd say the intended answer would be at least 3. Of course, you can have a gajilion permutations, but this would seem to be the lowest limit.
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Re: How many Birds  
« Reply #23 on: Mar 15th, 2014, 11:51am »
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If we reword the problem statement slightly:
 
How many birds are in a flock in which it's always possible for one bird to lead two and two birds to lead one?
 
then let's assume a steady state straight line constant velocity flock. In such a flock all the birds have identical velocity vectors - same length, same direction.
 
Since we need a metric to work with I propose a Flight Perpendicular (FP for short) - a perpendicular to a velocity vector through a bird. A bird is a leader then iff its, possibly forward-extended, velocity vector does not intersect any other FPs. In figure 1) B is the leader:
 

 
Leader's FP is the leadership line - line L in figure 1). Any bird on L leads. Any bird behind it - trails. A bird is behind if its, possibly forward-extended, velocity vector intersects at least one other FP. So in figures 1) and 2) one bird (B) is leading two (A and C) or two birds (A and C) are trailing.
 
When does a solo leadership of one bird end? If we keep rotating the velocity vector, counterclockwise in figure 2), we'll see that at some point at least one non-leading FP will merge with the leading FP - figure 3). In plain speak the condition is compound. When a straight line between any two birds is perpendicular to their velocity vectors and no other bird is in front of them then two birds lead.
 
If in figure 3) you mentally flip the velocity vectors 180 degrees the birds A and B are on the straight line that's perpendicular to their velocity vectors but they are not in the lead. In that case one bird (C) is leading two (A and B) or two birds (A and B) are trailing.
 
Let's see what will happen if we subtract and add one bird from/to the flock.
 
Subtraction. With a 2-bird flock we remain in 2D. Possible configurations are 1) two birds lead zero birds and 2) one bird leads one bird. Both configurations violate the problem statement.
 
Addition. With a 4-bird flock we may or may not leave 2D. Let's say we are still in 2D. Possible configurations are 1) three birds lead one, 2) two birds lead two and 3) one bird leads three. All three configurations violate the problem statement also.
 
To extend the 4-bird flock into 3D all we have to do is replace the perpendicular line with the perpendicular plane.
 
Finally, we have to exclude two colinear special cases. If the velocity vector is perpendicular to the common line then all 3 birds lead. If the velocity vectors coincide with the common line then in either direction only one bird can lead two and two can not lead one.
 
So with the above problem statement and definitions 3 birds, cocircular or colinear barring two special cases, is a unique solution.

 
If you fix the direction but allow individual velocities to take on different values during the flight then I think the answer should still be the same.
 
If both - value and direction - of individual velocities can change at any given time in an arbitrary way along an arbitrary curve/surface then it gets more complicated.
 
[edit]
Moved the drawing file to this forum.
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« Last Edit: Apr 5th, 2014, 8:25am by rloginunix » IP Logged
rmsgrey
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Re: How many Birds  
« Reply #24 on: Mar 17th, 2014, 5:19am »
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on Mar 15th, 2014, 11:51am, rloginunix wrote:
A bird is a leader then iff its, possibly forward-extended, velocity vector does not intersect any other FPs.

 
I object to this definition.
 
I would define leading as a relationship between pairs of birds - for any pair of birds, either A leads B or B leads A or neither leads the other.
 
With three birds: A, B, C, it's tempting to add the rule that if A leads B and B leads C, then A leads C, but extending that to higher numbers of birds rules out the scenario where the birds fly in a circle - in that situation, A would be leading B but B would also be leading A...
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