The Egg consists of differently colored parts.
Which is bigger - the total area of the light parts (yellow tones) or
the total area of the dark parts (blue tones)?

Provided with a perfect square, a pencil, a piece of paper your goal is to
use your creativity to draw a... perfect equilateral triangle. How hard is
it to convert a square into a triangle?

The same circle is simultaneously inscribed in one regular hexagon and
circumscribed outside another regular hexagon. Is this information
sufficient to determine the ratio of the hexagons' areas?

Imagine a steel belt is stretched tightly around a big planet. What things
can be possibly slipped under the belt, if a meter of steel added to the
belt raises it off the sphere's surface by the same distance all the way
around?

A disk of certain diameter is removed from a piece of paper creating a
circle hole in it. The goal is to calculate the area which still remained
around the hole.

What is the shortest trip for a spider to get from one spot on a
rectangular box to another? Does the straight and clear line that it seems
to be at first sight will be the shortest?

It is quite easy to get the cross sections in form of a square or a
regular triangle from a cube. Is it so easy to get the cross section of a
regular hexagon from the same cube?

The three rays that come through the three squares create the three angles. A
proof is required to be found that the sum of two angles equals the third
one.

It is known that a cylindrical hole six inches long is drilled straight
through the center of a solid sphere. Is this information sufficient for
calculating the exact volume remaining in the sphere?

It is required to dissect an obtuse triangle into acute triangles only.
The first question is whether it is possible at all? If the answer is
"Yes", then the next question would be "How?"

Figure out the diagonal of a
rectangle when it is inscribed in the quadrant of a circle. How long, do
you think, it will take you to get the right answer to this geometrical
question?

This geometrical problem is about an elegant and neat way how to figure
out the exact area of the overlapping of two squares. Don't you want to
discover this way by yourself?

Two lines are drawn on the two
sides of a cube. They are drawn form the same corner and the question is
which angle do these lines form? How to figure that out?