Puzzle time, count the hydras
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@Horace said in Puzzle time, count the hydras:
How do you deduce, from the information at the gate, collected over an arbitrarily long time span, x, y, and z?
Attach a color CCTV camera???
(Actually, I have no idea and no really sure where to start. I will think about it, but doubt I will be able to do the solution.)
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Nice framing of the problem, @Horace.
Kindly clarify this ... you say the "gate" will report whether it has seen "at least one" head of a certain color in the last minute. Does that mean, the gate is reporting only "one bit" of information for each color per minute (as opposed to reporting the number of heads for each color it has seen in the last minute)?
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@Axtremus said in Puzzle time, count the hydras:
Nice framing of the problem, @Horace.
Kindly clarify this ... you say the "gate" will report whether it has seen "at least one" head of a certain color in the last minute. Does that mean, the gate is reporting only "one bit" of information for each color per minute (as opposed to reporting the number of heads for each color it has seen in the last minute)?
Right. You get a binary for each head color, per minute. Either zero of that color passed through, or some positive number. But you don’t know how many.
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@Klaus said in Puzzle time, count the hydras:
@Horace said in Puzzle time, count the hydras:
How do you deduce, from the information at the gate, collected over an arbitrarily long time span, x, y, and z?
How do you deduce what exactly?
x y and z were defined in the problem. They are the rate of entry of 1-hydras, 2-hydras, and 1,2-hydras.
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We're actually pursuing a patent for this. One cannot patent a mathematical process, but our patent lawyers contextualize it into our physical instrumentation. They have some experience with this. They expect it'll get rejected at first pass, but maybe approved on appeal.
Maybe in a couple years I'll update this thread with the good news of a patent. But I would bet against it. -
@Horace said in Puzzle time, count the hydras:
We're actually pursuing a patent for this. One cannot patent a mathematical process, but our patent lawyers contextualize it into our physical instrumentation. They have some experience with this. They expect it'll get rejected at first pass, but maybe approved on appeal.
That makes sense. When you think about it, Google’s “search” algorithm is a mathematical process too, yet you can bet Google has all sorts of patents around it. It may take a few years to prosecute the patent, but congratulations on getting the patent application filed.