Combinatorial Game Theory
What is the name of the game we practiced with in the August meeting?
Hackenbush
A cell becomes alive if it has _ neighbors.
3
What is Euler's formula for polyhedra?
Number of faces + Number of vertices - Number of edges = 2
Where is the golden ratio found?
In art, architecture, nature, etc.
Name the two main application of Benford's law. Data science is not a valid answer for this question.
Error detection and tax fraud detection.
A positive result means ____ has the advantage.
Blue
A cell dies from isolation if ...
It has less than 2 neighbors.
Consider an equilateral mesh with vertices A,B, C inside an ABC triangle. Can the letters be assigned so there is not an ABC triangle on the inside?
No, this is impossible.
The concept of the golden ratio is originally based off of 2 ______________.
Line segments
What is another name for Benford's Law?
The Law of First Digits or the Phenomenon of Significant Digits
Explain the Tweedledee Tweedledum game theory tactic.
Copy the other player's moves.
What is a still life?
A pattern that is the same from one generation to the next.
The sum of the critical points of a topological surface is always ____.
2
What is the approximate value of phi?
1.618
Explain the connection between Benford's Law and winning the lottery.
What is the numerical result of this game scenario?
Extended time to 45 seconds!
-1/2
What is an oscillation?
A pattern that is stable over a cycle
Explain whether or not the objects in this transformation are topologically congruent.
No. Pasting together is not a valid topological transformation. Points in the output are closer together than in the input. This violates the rules of a topological transformation.
How do the Fibonacci numbers connect to the golden ratio?
The greater the pair of Fibonacci numbers, the closer the ratio is to the golden ratio.
What is the basic idea of Benford's Law?
In most numerical records, there is not a uniform distribution. Digit 1 is most common followed by 2, 3, 4, …. 9.
What is the numerical result of this game scenario?
Extended time to 1 minute!
3/4
List all 4 rules of John Conway's Game of Life.
1. A cell becomes alive if it has 3 neighbors.
2. A cell stays alive if it has 2 or 3 neighbors.
3. A cell dies from isolation if it has less than 2 neighbors.
4. A cell dies from overpopulation if it has 4 or more neighbors.
What are the three rules of a topological transformation?
1. Must be continuous
2. Must be invertible
3. Must have inverses that are invertible
What idea is the golden ratio based on? (Give your answer in terms of a and b).
a/b = (a+b)/a
What is the probability that the leading digit of a number will be n?
log base 10 (1 + (1/n))