

Interesting math puzzle - harder than it sounds - mschireson
http://maxschireson.com/2011/10/08/a-math-puzzle-thats-harder-than-it-sounds/

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dreamux
31 feet.

Ant jumps off the wall and onto the floor (no walking necessary, and easily
survivable), walk straight across the 30 foot floor and 1 foot up the wall.

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noblethrasher
Less than 31 feet since, in the presence of gravity, the honey is moving
towards the floor as well.

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mayoff
The answer, with a diagram, can be found here:

<http://mathworld.wolfram.com/SpiderandFlyProblem.html>

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losvedir
Ha, well that was a lot easier than I made it.

I ended up with the right answer by finding the minimum of the equation

    
    
        f(x,y) = 2(sqrt(1+x^2) + sqrt((6-x)^2 + y^2) + sqrt((15-y)^2 + 36))
    

which is the length of the path taken if the ant goes up to the ceiling at a
point x to the East of straight up, and from there goes to the side wall at a
point y to the south, and then goes from there to the center of that wall.
(And then it's mirrored).

I should have thought to unravel the room! Errr.

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tzs
To make the "minimize the equation" approach complete, other paths should be
considered, such as instead of going up to the ceiling, going to the side and
taking a side wall.

Some limits can be placed on the number of possible paths by considering some
general properties of an optimal solution:

1\. Assuming the start point is A, and the path leaves the start side at point
B, the optimal path will take a straight line from A to B. Proof: if it were
not straight, it could be replaced by a straight line which would shorten the
path, contradicting the assumption the path was optimum.

2\. Once the optimal path leaves a side, it will not return to that side.
Proof. Suppose the path leaves the side at point B, then later enters at C,
and then leaves again at D. The route from B to C could be replaced with a
straight line from C to D, which would shorten the path, again contradicting
the assumption that the path was optimum.

This cuts down the number of possible path templates greatly, since a given
surface can only appear once in the optimal path, and only contain a single
straight line segment.

I expect that a little more reasoning can deduce some more limits on possible
optimal paths, to get it down to just two or three possible equations to
maximize.

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mschireson
This one got my kids a bit interested but not enough to get them really
engaged in trying to solve it. Anyone have fun puzzles for middle-schoolers?

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byoung2
40 feet?

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akavi
I'm pretty sure this is the correct answer too.

Visualization tip: Consider the possible nets of the rectangular prism that
makes up the room, and find what the shortest path on one of them would look
like.

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mschireson
Its the best I've found.

Another way of thinking about the visualization is to make a model of the
surface that can fold up to form it. The shortest path (which will be a
diagonal if not a straight line) on any of those is the answer.

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Eduard
Does the ant have wings?

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mschireson
No, it does not. And while someone suggested that it could drop to the floor
without injury, you could consider it to be afraid to do so :)

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dredmorbius
0 feet.

It's a flying ant.

