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"Phase ambiguity" puzzle

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(@dave-lindell)
Posts: 1683
Topic starter
 


(And show your solution)

 
Posted : March 25, 2015 7:33 pm
(@dave-lindell)
Posts: 1683
Topic starter
 

Puzzle TTT

200 views and no solutions???

 
Posted : March 30, 2015 9:17 am
(@moe-shetty)
Posts: 1426
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Puzzle TTT

two hundred other things to do. i want to solve it, but just can't pick up a habitual puzzle like that

 
Posted : March 30, 2015 10:04 am
(@bill93)
Posts: 9834
 

No nice solution occurs to me, so I brute forced it. I plotted the points on paper and drew circles of the various radii, e.g., for A I plotted 10.880 meters, 12.880 meters, etc.

After drawing a few circles from some of the points I saw that they were all intersecting near one spot, so that gave me integers to try. I put the resulting distances in least squares and found the best fit had residuals on the order of 1 mm.

I'll post values later, so as to not kill the incentive for others. I'll be very interested in a "proper" solution method.

 
Posted : March 30, 2015 12:25 pm
(@bill93)
Posts: 9834
 

T= North 636.0000, East 342.0006
Integer and distances from T:
a = 6 12.881
b = 8 17.054
c = 7 14.384
d = 6 13.791
e = 7 14.944
f = 5 10.865

So how were we supposed to do it?

 
Posted : March 31, 2015 3:36 am
(@bill93)
Posts: 9834
 

Still need a solution method

I'm still waiting for a hi-brow solution method.

 
Posted : April 7, 2015 11:12 am
 vern
(@vern)
Posts: 1520
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Still need a solution method

I solved it with CAD.
I noticed in your previous answer post that two actually 3of the answers are not technically correct. The marker must be an even number... 2 4 6 8 etc.

 
Posted : April 7, 2015 11:35 am
(@bill93)
Posts: 9834
 

Still need a solution method

It depends on your definition of the integer. Mine are the integer number of 2-meter "cycle" distances, not the (even) number of meters you would read from the tape. The integers are multiplied by 2 meters and the reader distance is added to get the total distance.

How, more specifically, did you use CAD to solve it?

 
Posted : April 7, 2015 12:58 pm
 vern
(@vern)
Posts: 1520
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Still need a solution method

I placed the points with known coordinates and drew circles around them with radius of the "add" distances. I just started offsetting the circles 2 meters until they all intersected.

 
Posted : April 8, 2015 1:14 pm