Stepping Stones Puzzle Concepts

The video introduces the stepping stones puzzle, created by Michigan State undergraduates. It involves placing brown and white stones on an infinite chessboard, following specific rules. The goal is to determine the maximum number of white stones that can be placed, given a set number of brown stones. The video demonstrates solving the puzzle with two brown stones, reaching a maximum of 16 white stones. It explores configurations, theoretical limits, and provides a mathematical analysis of the puzzle's upper bounds.

What is the main objective of the stepping stones puzzle?

• To place stones in a spiral pattern

• To place as many brown stones as possible

• To achieve the highest number with white stones placed in order

• To cover the entire chessboard with stones

In the puzzle, when can you place a white stone labeled '2'?

• When it is placed at the edge of the board

• When it is surrounded by four brown stones

• When it has two neighboring squares of value 1

• When it is adjacent to a stone labeled '3'

What is the highest number achievable with two brown stones?

• 18

• 14

• 16

• 20

What is the known result for the maximum number achievable with four brown stones?

• 28

• 38

• 60

• 49

What is the main challenge in finding the configuration for seven brown stones?

• The rules change for seven stones

• No one has been able to work it out yet

• The stones are not distinct

• The board is too small

According to Andrew Howroyd's construction, how many additional steps can each brown stone provide?

• Six

• Five

• Four

• Three

What is the formula for the lower bound of the puzzle's growth?

• 6n - 5

• 5n - 4

• 3n + 2

• 4n - 3

What is the theoretical upper bound for the maximum number achievable with n brown stones?

• 1000n

• 500n

• 714n

• 300n

What is the significance of the number 65,000 in the context of the puzzle?

• It is the number of configurations possible with three stones

• It is the number of stones needed to cover the board

• It represents a theoretical high point used in an argument

• It is the maximum number achievable with two brown stones

What does Robert Gerbicz's argument suggest about the puzzle's growth?

• It grows linearly

• It grows exponentially

• It has a quadratic growth

• It has a logarithmic growth