On the Complexity of the Linear Sliding-Coin Puzzle

• Main Authors: Lin, Ting-Yu, 林庭宇
• Other Authors: Tsai, Shi-Chun
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/96920020639531182613

碩士 === 國立交通大學 === 資訊科學與工程研究所 === 98 === Consider a line of n nickels and n pennies with all nickels arranged to the left of all pennies, where n >= 3. The puzzle asks the player to rearrange the coins such that nickels and pennies alternate in the line. In each move, the player is allowed to slide k >= 2 adjacent coins to a new position without rotating. We prove that it takes at least n moves to solve the puzzle, and present algorithms to generate the optimal solutions for k = 2 and k = 3. We also propose a framework to extend solutions, and apply it successfully to construct optimal solutions for k = 4 and k = 5.