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You are in the desert. You are instructed to get to the middle point between to visible marks far from you (meaning you can see them - see the direction to them - but you do not know how far are they from you). Suggest the best strategy that will allow you to determine how to get to the desired location between the two marks (middle) in the dessert as fast as possible - in other words, what is the shortest path you could choose?

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closed as unclear what you're asking by Engineer Toast, Gamow, Deusovi Aug 11 '16 at 2:20

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    $\begingroup$ If we are allowed to do one step to the side, we can use triangulation to figure out how far the points are away, and then go straight to the middle. Instead of restricting what we can determine, how about you reformulate the puzzle to restrict in what ways we are allowed to move? $\endgroup$ – Anon Aug 7 '16 at 23:28
  • $\begingroup$ Using parallax, we can easily take measurements from two points and then know exactly where the marks are. $\endgroup$ – Deusovi Aug 7 '16 at 23:29
  • $\begingroup$ This is not the most effective way, since it introduces potential for large error. I will modify it to the "best" strategy. $\endgroup$ – Moti Aug 8 '16 at 0:14
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    $\begingroup$ @Moti: You never said anything about error. Where does the error come in? $\endgroup$ – Deusovi Aug 8 '16 at 0:58
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    $\begingroup$ "get to the desired location between the two marks (middle) in the dessert as fast as possible" - If there is dessert there, do we need to worry about triangulation? :P $\endgroup$ – naffarn Aug 10 '16 at 0:08
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Assuming you are not already in line with the two marks, just walk along the imaginary line that bisects the angle between you and the two marks. Follow this line (which may be gently curved depending on your starting point relative to the two marks) until you are in line with the two points (at which time you have reached the 'middle'). This is a 'practical' answer in the sense that you could do it in practice. Update: But not practical in the sense that it doesn't get you to the right place...need to think about this a little more

If you want the absolute shortest path. Then take two infinitesimal steps at right angles and, by the change in angle of the two marks, use triangulation to determine the whereabouts of those points and the 'middle' then walk directly towards the middle. Your path will then be the straight line distance to the 'middle' plus 2x the infinitesimal step distance (which limits to zero as your steps get more and more infinitesimal...)

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  • $\begingroup$ As you said this is not the shortest path. Assume the points are long range from you. There is a way to do it without measuring angels. You only need to find the middle of segments and find points that are aligned on same line. $\endgroup$ – Moti Aug 9 '16 at 20:49
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    $\begingroup$ It is hard to measure angels as they are very small (It is believed that many can fit on the head of a pin). $\endgroup$ – Penguino Aug 9 '16 at 21:36

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