Enumeration of Standard Puzzles

TL;DR

This paper introduces a broad family of combinatorial objects called standard puzzles, providing explicit enumeration formulas and linking them to classical mathematical sequences like binomial coefficients and Fibonacci numbers.

Contribution

It defines standard puzzles and derives explicit enumeration formulas connecting them to well-known combinatorial sequences.

Findings

Enumeration formulas expressed via classical numbers

Connections established between puzzles and binomial, Fibonacci, tangent, and Catalan numbers

Framework enables systematic study of puzzle enumeration

Abstract

We introduce a large family of combinatorial objects, called standard puzzles, defined by very simple rules. We focus on the standard puzzles for which the enumeration problems can be solved by explicit formulas or by classical numbers, such as binomial coefficients, Fibonacci numbers, tangent numbers, Catalan numbers, $\ldots$