bonanova

Here's what I think.

Yes. Nicely done. And the obvious next question, what are the coordinates of that point? The star is twinkling.

There's more than meets the eye here. I've gone back and forth and concluded a couple things. It's a very nice puzzle.

I read this somewhere ... it seemed interesting, so I thought I'd share: Some time after Salvador Dali’s death, his younger brother became famous as (believe it or not) a surrealist painter. This younger brother had great international success and the word genius was used to describe him. His name was Dali and he did not change it. Yet today, the word remembers only one Dali and few even know he had a brother. Why is this?

Good Job, Cap'n, you've lowered the bar for M, giving her time for a little touch-up for the reporters sure to be at the shore covering the story for CNN. Can you go beyond 5%?

Are you taking into account that a sonic boom sweeps along the ground at the speed of the plane that generates it? Or are we to assume the sound originates from a fixed point and propagates at its native speed?

An ant walks East a distance of 100 feet. Next he walks north a distance of 50 feet. Then west for 25 feet, and so on. He keeps turning left and halving his previous distance. We know this geometric series converges. His path encloses a single point - the only point to which he will come arbitrarily close. One question that might be asked involves an infinite series: What is his total path length as he approaches the limit point? A more interesting question can be answered without a lot of math. What is the inclination [angle] from due east, of the line drawn back to his starting point? There are several ways to determine the second question. A coveted bonanova gold star will be awarded to the most elegant solution. Enjoy

By circle, which is a locus of points, we assume you mean disc, which includes the interior points.

This looks promising. How much advantage might be gained?

Leave it. And change the poem to read, When I am old I will become purple. Working on an answer. You would have to invoke calculus... The simple answer, which is wrong but permitted by an inaccurate reading of the OP, is don't worry, the pool will be fine before the guests arrive.

Wow ... in puzzles as in life.

The ogre will try to be on the shore where the boat lands before the boat gets there. It is a game. Whoever gets to that point first wins. The rower and ogre each act in their own best interest. The rest is part of the puzzle. The rower can row anywhere on the lake and the ogre can run anywhere on the shore. Assume each can turn on a dime [infinite acceleration, maximum speed.] Best strategy pursuit means to imply that the ogre will not lie down and take a nap. And the specific question now is Can the rower overcome a ogre speed ratio of greater than (1 + pi)?.

We have a sufficient condition. Escape is possible if the ogre's speed ratio advantage is not greater than [ 1 + pi ]. Is it also an necessary condition? I.e. can she escape if the speed ratio is higher? How much higher? That's the "twist" mentioned in the title.

Since it's solved, I won't spoiler this. The answer is not complex. Every birth, regardless of anything that is said, done, legislated, prohibited, presupposed, calculated, imagined or hoped for, has equal chances of being a boy or girl. If you flip a coin an odd number of times, then, yes, the number of heads and tails cannot be equal. But the question is for large numbers of conceptions and births - for a society - where, even though the numbers of boys and girls may not be exactly equal at every moment - each birth changes the running total - the chances of an excess of boys exactly equals the chances of an excess of girls. The question asks whether a birth control strategy can affect the society's overall gender balance in a systematic way. The answer is no, it can not. No calculus needed.

It's of a chestnut genre. But the solution is specific to the numbers provided, and I have yet to work through one of them. Have at it.

Nice problem. Are you sure she has to row that fast?

That is the way I read the OP Cap'n. But it may be the case that a forward-moving minute hand stops the hour hand, while a backward-moving minute hand starts the hour hand again. I think one of these interpretations precludes and answer, and that might make the OP as it stands a double puzzle.

I think there is a discrepancy with bonanova's answer because... Sure. The gender distribution within families is terribly skewed. A family can have an unlimited number of boys; a family can never have more than one girl. A family can have a girl with no brothers [half!]; a family can never have a boy with no sisters.

An ogre with a top land speed of 4 mph, but incapable of swimming, stalks the shore of a circular lake. The fair maiden out in the boat can outrun the ogre on land, but her rowing speed is nothing to write home to mother about. How fast must she be able to row to effect an escape? Make the assumption that the ogre is hungry [or otherwise desirous of the girl] and uses a best-strategy pursuit.

I learned calculus once. I remember using the word integral correctly in a sentence. For most of my career I used algebra and computers to solve problems. Since retirement, I differentiate, but only in the logical sense. I am in awe that SP did what he did; I understand what the Cap'n did.

* Handing Y-San an Excedrin, just for emergencies ...