I agree that middle-schoolers are quite bright individuals...and even younger than that!
When I was just 7 years old, I wrote out my theory of how the planets formed by the accretion of dust particles (I still have the paper!), only to be laughed at by my science teacher. Many years later, that same theory was embraced by cosmologists...never underestimate a child's imagination!
I'm with the middle schoolers. The question that interests me is - what are we doing with our middle schoolers to turn them into high schoolers? The difference in the two choices says to me that somehow we're maybe knocking the stuffing out of them.
In that case, there are engineers that exist only on paper (i.e. have the degree and PE license), and there are engineers that exist in practice (technicians, mechanics, and many others with less formal training).
Mr VectorForce, please put your engineering hat on, develop a design that fits the problem at hand, and declare that your first step will be 512/1023 of the distance to the target, then your steps will be
512, 768, 896, 960, 992, 1008, 1016, 1020, 1022, and finally 1023 parts of the 1023 divisor. QED! Our job as engineers is not to question IF it can be done, but determine HOW to do it.
A mathematician, a scientist and an engineer are given with a problem to resolve for a great prize. They can take up to 10 steps to reach a target, but each step must be no greater than half the size of the previous step.
The mathematician declares it mathematically impossible.
The scientist says it appears impossible but will try it, which he does and proves it's impossible.
The engineer thinks a bit and says "ten steps gives us an answer to better than 0.1%, which is within reasonable measurement tolerances for this problem, I claim the prize".
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