Computational Complexity of Generalized Golf Solitaire

Abstract

SUMMARYGolf is a solitaire game, where the object is to move all cards from a 5 × 8 rectangular layout of cards to the foundation. A top card in each column may be moved to the foundation if it is either one rank higher or lower than the top card of the foundation. If no cards may be moved, then the top card of the stock may be moved to the foundation. We prove that the generalized version of Golf Solitaire is NP-complete.

Choco Banana is NP-complete

“…After the publication of this book, a lot of Nikoli's pencil puzzles were shown to be NP-complete. Recently, Double Choco [3], Five Cells and Tilepaint [5], Sukoro [6], Tatamibari [2] Yajisan-Kazusan and Stained Glass [7] were shown to be NP-complete. for each 𝑐 𝑗 ∈ 𝐶 and (ii) the graph 𝐺 = (𝑉, 𝐸), defined by 𝑉 = 𝑈 ∪ 𝐶 and 𝐸 = { (𝑥 𝑖 , 𝑐 𝑗 ) | 𝑥 𝑖 ∈ 𝑐 𝑗 ∈ 𝐶 }, is planar.…”