Answer to Crystal Lake

Well, one plank alone isn't going to do it; the plank is more than three feet too short. But what about two? If one plank is laid diagonally across the the corner of the lake, you have, in effect, moved part of the shore closer to the center. Is it enough?

Let's see... the lake's diagonal is a little over 56 feet, so the distance from one corner to the island is going to be about 28 feet. If the plank laid in the corner just barely touches land at both ends, forming a right isosceles triangle, with the plank as the hypotenuse. The center of the hypotenuse is therefore eight feet from the corner of the lake. And unfortunately, twenty feet from the island. Ouch, we're no closer than when we started!

But by laying down the plank across the corner we have " shaved off" the corner of the square making it " rounder". What if we continued?

Laying two more planks over the obtuse angles created between the hypotenuse and the longer sections of the shore (this sounds confusing; it's obvious if you draw it out, or if you're feeling lazy, look at the pretty picture below), two new "shores" are created. A third plank connecting these two (parallel to the first) reduces the shortest distance to the island to under 16 feet. And you're there!

Now how to carry this monstrosity home...

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