## Mathematics and Computer Science

#### Event Title

Modern Algebra of The 15 Puzzle and Topspin

#### Document Type

Oral Presentation

Indianapolis, IN

#### Subject Area

Physics, Mathematics & Computer Science

#### Start Date

10-4-2015 10:15 AM

#### End Date

10-4-2015 10:45 AM

#### Description

The 15 Puzzle is a 4x4 puzzle with 15 pieces numbered 1 through 15 and one blank space. To solve the puzzle, one must slide one piece at a time until the pieces are in numerical order and the blank space is in the 16th spot. Topspin is a puzzle consisting of 20 pieces numbered 1 through 20 that form an oval track. To solve the puzzle, one must manipulate the order of the numbers by flipping the turnstile holding 4 pieces and by shifting the numbers around the track until the pieces are in numerical order. I will be discussing the mathematics behind the 15 Puzzle and TopSpin, including why these puzzles work and how to know up front if the puzzles are solvable. I will also include algorithms to solve the puzzles and explain how these algorithms relate to the symmetric group from Modern Algebra.

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COinS

Apr 10th, 10:15 AM Apr 10th, 10:45 AM

Modern Algebra of The 15 Puzzle and Topspin

Indianapolis, IN

The 15 Puzzle is a 4x4 puzzle with 15 pieces numbered 1 through 15 and one blank space. To solve the puzzle, one must slide one piece at a time until the pieces are in numerical order and the blank space is in the 16th spot. Topspin is a puzzle consisting of 20 pieces numbered 1 through 20 that form an oval track. To solve the puzzle, one must manipulate the order of the numbers by flipping the turnstile holding 4 pieces and by shifting the numbers around the track until the pieces are in numerical order. I will be discussing the mathematics behind the 15 Puzzle and TopSpin, including why these puzzles work and how to know up front if the puzzles are solvable. I will also include algorithms to solve the puzzles and explain how these algorithms relate to the symmetric group from Modern Algebra.