BrainDen.com - Brain Teasers

bonanova

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1. Hitting a double

"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
2. Who should do what

Logophobic has it.
3. Hitting a double

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.
4. Making a spiral

Agreed. Quite a bit off. Upon further review my guess (of a cosine relationship of line angle to wall angle) was wrong.
5. How many spin-able numbers are there from 0 to 99999 ?

I think Logophobic has it.

Here's why:
7. Rolling on a sine curve

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,

12. Guessing right number from 1 to 27, with 3 Yes/No/Maybe questions.

First thoughts:
13. 5x5 statement table.

Nice puzzle, jasen. Do you have more like this?
14. A paradox? of two chests

Here's a refutation based on the impossibility of having chests whose value has uniform probability across the real numbers (or integers.)
15. A paradox? of two chests

I'll give a refutation by symmetry. Mainly because Bayesian formulas are opaque to me. (Read, I tried to understand a priori distributions once.) Your first choice is random. If you switch you end up the the choice you would have made, with 50% probability, without switching. Your expectation for either envelope is \$1.5x, where \$x is the lesser of the two amounts. OK, yeah, the faulty argument in my post above presumes a uniform probability on the real numbers for \$x. Anyone who thinks \$2 and \$Graham's Number have equal probability needs to immediately make a random deposit into my checking account. (Account number supplied upon request.)
16. Math puzzle

This was a fun puzzle.

20. 5x5 statement table.

I assume "surrounded by" means "adjacent to." So do diagonals count?
21. Help the police to reveal the hidden password.

Before reading the file I immediately thought of one method.
22. Distorted rectangular prism

It depends on what is constant and what can vary. Do the edges all keep their original lengths? Does the cross section remain everywhere square? By "connecting 8" edges" do you mean deforming the shape and "gluing" the square faces to each other, a to b, b to c, c to d and d to a so that the new shape has no vertices (corners)? Do the 8" edges end up as circular arcs? What keeps us from doing this and then squashing the final shape flat so that its volume is zero? I can't visualize a process that gives a final shape having a definitive volume.
23. Distorted rectangular prism

Are we looking at the back and front 4x4 faces from the same direction? Or, does left and right, as they refer to the back face, assume we have turned the shape around so we're looking at outside of the back 4x4 face? That is, if we label the vertices ABCD on the front face, clockwise starting from the upper left corner like this A B D C Then if the 8" edges connect these to the back face vertices EFGH as A-E, B-F, C-G, D-H would your connections be A to H, D to G, and so on? It sounds as if we are joining the front and back faces of a prism to form a torus that has a square cross section, only we're twisting the shape by 90 degrees before joining the faces. (Kind of like constructing a Mobius strip from a piece of paper. This new shape would have only three sides, just as a Mobius strip has only one side. Interesting.) I wonder, though, with the length (8) being only twice the side (4) whether this is even possible. One thought:
24. Mega Einstein Riddle

I noted the number(s) of the clue(s) that refer to each of the items. This is making it easier to piece together little clusters of relationships. Next I'm trying to fit these clusters into a table where one column is filled in (e.g. house numbers). Or probably into several tables, each with a different column filled in, depending on the "shape" of the clusters. It's a huge puzzle any way you look at it.
25. Mega Einstein Riddle

Thanks for the category lists and clarifications. This is actually a favorite style of puzzle, and I can see myself enjoying it for a while. @Thalia, Game on ...
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