Let's say that I'm in a rectangular field,2 miles in width and 3 in length, with a metal detector. I know that somewhere within this field lies a penny, which is equally likely to be at any point. My metal detector will detect any penny within a 30-ft radius of my location. Furthermore, this penny is the only metallic object in the field (at least as far as my metal detector is concerned). I want to minimize my metal detector's battery usage. Of course, I'll turn off my metal detector when I walk back to a place I've already been to.
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- $\begingroup$ What is the definition of efficient here? Because if it's just battery use, then how is it spent? If I turn it on for a moment, do I get to detect anything within 30 ft instantly? Then I could walk around, flip it on for an arbitrarily small time, and then move elsewhere. That seems trivial, though. $\endgroup$Zach Stone– Zach Stone2016-01-14 03:06:35 +00:00Commented Jan 14, 2016 at 3:06
- $\begingroup$ "Efficient" simply means using as little battery life as possible. Also, the metal detector detects metal as soon as it is turned on. However, what I want is for the detector to be on somewhat continuously. $\endgroup$moonman239– moonman2392016-01-14 22:30:45 +00:00Commented Jan 14, 2016 at 22:30
- $\begingroup$ Unless you have something more specific than somewhat continuos, I don't really know how to help. Optimization is all about edge cases. So defining the limitations is a critical part of the problem. $\endgroup$Zach Stone– Zach Stone2016-01-15 03:38:39 +00:00Commented Jan 15, 2016 at 3:38
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1 I was thinking something like this. Basically we divide a rectangle into halves, eighths, etc. until we find what we're looking for.
First, I walk along each each diagonal Second, I walk along the center lines of the rectangle and thereby divide the rectangle into smaller rectangles. I then repeat these two steps with each rectangle until I find the penny.
- 1$\begingroup$ You should have included this as part of the question, since these are thoughts and not a mathematical answer. It is a nice question, by the way. $\endgroup$Shailesh– Shailesh2016-01-14 02:27:02 +00:00Commented Jan 14, 2016 at 2:27