Genady

You haven't mentioned that the decimal system has a special significance in your theory. Does it?

Correct. +1

Hmm ... Except the twin paradox has nothing to do with the Doppler effect. It has to do with the time dilation. The latter is the same regardless of direction of the motion. It depends only on the relative speed between two frames of reference.

What fraction of the bottle is full?

Fixed. Another bottle puzzle:

Will not this work: How to Break a Glass Bottle Safely (ehow.com)?

Like a garbage bag?

It reminded me of a puzzle with two racing bugs. One goes up and down a wall with constant speed. Another goes up, to the same height, with the half speed and then down with the double speed. Who wins? The first bug wins. It is back to the starting point by the time the other one just gets to the top.

Exactly. Intuition without a little arithmetic does a bad job here. +1. (I didn't know about Murphy, and it took me longer to figure it.)

Precisely. +1

A car goes 15 mph for 1 mile. How fast must it go in the same 1 mile back to average 30 mph for the entire round trip? *According to a story, Albert Einstein got this puzzle in a letter from a friend and enjoyed the trick.

I guess, it will be a secret, like the rest of it:

Trump. Here is a quote from Beneath contempt Definition & Meaning - Merriam-Webster:

Yes, this is right. +1. Around the equator, I have estimated it like this: I hope my reply above would clarify.

Exactly correct. +1. (May I ask you to hide your answer using Spoiler button next time as the question is in this forum?)

This is correct. +1 I don't know a way with fewer cuts.

How do I know? Ask OP:

Perhaps you can demonstrate it by solving the unsolved puzzles here: Brain Teasers and Puzzles - Science Forums

You can enlarge other parts of your body as well. Just Google it.

During Solar eclipse the Moon shadow moves on the Earth surface. In which direction does it move, toward East or toward West?

It is demonstrated here:

What can I say without being banned? Ha-ha.