bonanova

That's an interesting approach to solving a problem, but I guess what remains to be proven is

Hands well waved. But here's a clue for another answer.

Yes, these are the complete set. The last one has a simple explanation. Can you find it?

There are more.

So the Ogre and the Maiden problem is actually a solution/approximation method for tan(x) = x + π. So on top of your last graph you would plot f = cos a and get both f and a at the intersection. Very cool. Using the other equations you would intersect tan a with a + pi to get a, then take cos to get f. An extra step.

Here's a quickie ... should take about a minute. If you draw four points on a paper, no three of them collinear, they define six line segments. If the points lie on the corners of a square, four of the segments are of length 1, say, and two are of length sqrt(2). How many different configurations of four points give edges whose lengths are one of two values?

This is not a puzzle but an observation of something that to me was surprising. Two unrelated puzzles - the and the problem, succumb to identical analyses. Both present an equation that does not have an analytical solution for a crucial angle, let's call it x. The equation that presents itself is this: tan(x) = x + k where k is some constant, and x is expressed in radians. You can't get a general solution x = x(k), but you can solve the equation iteratively for x for any particular value of k. When that is done, the the desired answer turns out to be cos(x) = answer. I wonder whether there is a prototypical problem for which this is the best analysis? Did this post turn out to be a puzzle after all?

Assuming the kite was vertically and horizontally symmetric, because you don't say where the sticks cross,

He doesn't travel. He's already there.

I'll bump this unanswered puzzle, and wait for an answer that I cannot even imagine.

BMAD, you're giving us a nice selection of new puzzles. Not to worry if there is a duplicate. Full disclosure, I have reposted my own problems, on at least two occasions. a) bad memory b) I loved the problem c) search words were not well chosen d) all of the above. Answer: d. kman, good catch, and I will close this topic.

Hi tammie, and welcome, if no one else has said it, to the Den. Yes, you have it right. There are 12 trees. Eighteen rows have 3 and only 3 trees in them. There is a "bonus" row, if you want to call it that, and it has 4 trees.

I guess we can assume by "round person" that your waistline approximates a circle. We need to know the original or final size. RG's answer is the correct one if you reduced down to a zero waist. I'm looking at this problem assuming you started out as *gasp* 40" waistline..

I have finished a rigorous proof that the tangent to the inner circle is the best path, straight or curved, that permits the girl and boat to reach shore safely, with the lowest speed ratio compared with ogre, namely 0.2174, or 1/4.6003. ogre1.doc It shows also that reversing direction is not part of either Ogre's or the girl's best strategy. Does it cover all the bases?

Yeah, that's it. Nice. The site is a little hokey lately.