Game Theory Problem dealing with personal choices

This is a problem dealing with game theory and personal choices

Cutting a Cake-Game Theory Problem dealing with personal choices

Problem dealing with cutting a cake and personal choices

Allocation between two persons of a list of items and their preference

This is an allocation of ten estates between two individuals

Statistics

"When the members of the Eye and I Photo Club discussed what type of film they had used during the past month, the following information was obtained; 77 used black and white film, 24 used only black and white, 65 used color, 18 used only color, 101 used black and white or color, 27 used infrared, 9 used all three types, and 8 d ...continues

Modern/Abstract Algebra Problem (Group Theory)

Show that the group generated by two elements where all the elements have order 3 is finite.

Modern/Abstract Algebra Problem (Group Theory)

What is the number of different conjugated classes of elements of order 2 in S_5.

Modern/Abstract Algebra Problem (Group Theory)

What are the normal subgroups in S_4.

Modern/Abstract Algebra Problem (Group Theory)

What are the normal subgroups in S_4. I would appreciate it if someone could also a thourough explanation of how they came up with the answer.

Deduction of the addition theorems for trigonometric functions as the simplest consequence of the representation of complex plane's rotational group.

Deduce the addition theorems for trigonometric functions:

Central Extension Problem

Describe all nonisomorphic central extensions of Z_n by Z_2 x Z_2 meaning central group extensions of the following form 1 --> Z_n --> G --> Z_2 x Z_2 --> 1 Meaning, determine those nonisomorphic groups G that can be described by such an extension. Please also explain how you came up with the answer.