Estimate the mass of the gravitational field of the Earth. What would the size of a cube of water with the same mass?

Use the following info (the real info is complex, but the following is close enough):

Relative density of inner core = 13, radius = 400 km

Relative density of outer core = 11, radius = [...]

The Darkside of the moon receives some twilight like we do on Earth, but ignore that, assume it is dark since there no atmosphere to color it’s sky.

Make you best estimate, by percentage during our Earth day of 24 hours, what percentage of the Darkside is completely dark?

A ball is dropped from a height of 1 m on to a hard surface. Each time it bounces, the ball loses half of it’s energy. How long does the ball bounce for? Is there a paradox?

Let a and b be two irrational numbers. Is it possible that a^b is rational ?

This page is for information only. It will experience “creeping beauty” over time.

You are welcome to post on it, but I will edit, delete, merge it as I see fit.

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I’m (generally) only going to deal with the positive integers. Including the negative integers (and 0) makes for a lot of pain for [...]

This problem made me think of Chris. Actually I am performing this is Excel for our National USA Soils Office. Our Soil Scientists investigate surface soils and map the specific types. For a specific mapped area they do transects and record info like this… This point is A, next point is C, this point is B… then [...]

Infinitely many coins coins are aligned, with heads facing up.

1 – Then, all coins are flipped.

2- Then, the second, fourth, sixth, … are flipped.

3- Then, the third, sixth, ninth,… are flipped.

…

k- Then, coins numbered k, 2k, 3k, … are flipped.

…

After this infinite process is done, what is the proportion of the coins numbered p, p^2, [...]

Given the string 123456789101112, in how many different ways can you place “+” signs among some of the digits, so that the overall expression sums up to 2013?

The answer is at least 1, due to Zorglub’s example: 12+34+56+789+10+1112 = 2013