bonanova

Yeah, that's it. I have an online tree now (ancestry.com) with a few thousand names. I get inquiries and "matches" almost daily from people who descended from an uncle's sister-in-law of an 8th-generaltion direct ancestor. Soon you realize how interconnected the human family is. The gene pool is constantly being stirred. Even if you could map the whole thing you'd need a lot of color coding to discern in individual's tree. We'd all be different colors simultaneously, and a lot of "branches" would be tied into knots. (Rednecks all... )

I get that. I thought it was strange that the question was introduced with an "overpopulation" flavor. (Maybe it was just a red herring.) My comment badly implied that yours wasn't responsive to the question; I meant to opine that the introduction wasn't all that germane. There are a couple of "paradoxes" when one considers family trees and such. For example we all have two parents, four grandparents, eight GGPs, sixteen GGGPs, and so on. So how is an exponentially increasing heritage as we go back in time consistent with a growing population going forward? Was there an original, parenting "couple" N generations back? If so, how could they singly play all the roles of my 2N progenitors at that time? And, if two kids/family going forward gives a stable population, how can it also produce an exponential personal progeny? I found Mitochondrial Eve an interesting read.

Brute force Has anyone found a constructive solution?

"... for a thousand years. How many descendants would you have?" But we're not enumerating the world's population. We're quantifying the part of it that comprises your descendants. Two children, four grandchildren, ...

Give it a try:

Doesn't each birth increase the population? What if, miraculously, no one will die? But the question does not hinge on when/whether people will die. The question asks: how many descendants will you have?

@BMAD The three of us: you, I, and Logo, agree on the 5 4 1 5 3 = 18 assignment. I like your approach, where the solution can be constructed.

Can we see it?

A quick and dirty analysis

Nice puzzle.

First thought

It might be solvable, iteratively. I once posted a puzzle, here or elsewhere, that went as follows: But in that puzzle information was added as the constraints were iteratively applied. Here it seems it must all be determined in one shot. So maybe that's not possible.

"Determine the rate of change to second base once the runner reaches halfway to first base." Determine the time rate of change of the distance between the runner and 2nd base when the runner is halfway between home plate and first base, running at 24 ft/sec on a path that is a straight line from home plate to first base. If these two statements ask for the same information, then

Logophobic has it.

Of his position? Of his velocity? Most runners going to 2nd base will swing wide to round out the corner and keep a constant speed.

Agreed. Quite a bit off. Upon further review my guess (of a cosine relationship of line angle to wall angle) was wrong.

I think Logophobic has it.

Here's why:

Yes I agree. If the coin centers follow different-length paths, the shorter path will be traversed first. And since the radii are not zero, then even if the sine wave is in light-years the coin following the concave side of the curve will arrive first. (See my "In any case" post.) In the limit as the ratio of radius to amplitude goes to zero, however, the paths of the centers (and their transit times) coalesce. I just wondered if there were a reason to give units to the diameters (and not the amplitude of the sine wave.)

Looks like

In any case,

Clarification, please.

First thoughts:

Nice puzzle, jasen. Do you have more like this?