This paper extends the work started in 2002 by Demaine, Demaine and Verill (DDV) on coin-moving puzzles. These puzzles have a long history in the recreational literature, but were first systematically analyzed by DDV, who gave a full characterization of the solvable puzzles on the triangular grid and a partial characterization of the solvable puzzles on the square grid. This article specifically extends the study of the game on the square grid. Notably, DDV's result on puzzles with two "extra coins" is shown to be overly broad: this paper provides counterexamples as well as a revised version of this theorem. A new method for solving puzzles with two extra coins is then presented, which covers some cases where the aforementioned theorem does not apply. Puzzles with just one extra coin seem even more complicated, and are only touched upon by DDV. This paper delves deeper, studying a class of such puzzles that may be considered equivalent to a game of "poking" coins. Within this class, some cases are considered that are amenable to analysis.

翻译：本文延续了Demaine、Demaine与Verill（DDV）于2002年提出的硬币移动谜题研究。这类谜题在娱乐数学文献中历史悠久，但DDV首次对其进行了系统分析，完整刻画了三角网格上的可解谜题，并部分刻画了方格网格上的可解谜题。本文专门扩展了对方格网格游戏的研究。值得注意的是，DDV关于"两枚多余硬币"谜题的结论被证明过于宽泛：本文给出了反例并修订了该定理。随后提出了一种解决两枚多余硬币谜题的新方法，该方法覆盖了前述定理不适用的某些情形。仅含一枚多余硬币的谜题似乎更为复杂，DDV仅略作提及。本文对此进行深入探究，研究了一类可视为"戳硬币"游戏的谜题，并分析了其中若干可解情形。