Generalized Rascal Triangles

TL;DR

This paper introduces a broad class of number triangles called Generalized Rascal Triangles, characterized by arithmetic sequences on diagonals and specific multiplication and addition rules, extending the original Rascal Triangle concept.

Contribution

It generalizes the Rascal Triangle by defining new triangles with arithmetic diagonal sequences and Rascal-like operations, expanding understanding of these structures.

Findings

Characterization of Generalized Rascal Triangles by diagonal arithmetic sequences

Establishment of Rascal-like multiplication and addition rules for these triangles

Extension of the Rascal Triangle concept to a broader class of number triangles

Abstract

The Rascal Triangle was introduced by three middle school students in 2010, and in this paper we describe number triangles that are generalizations of the Rascal Triangle and show that these Generalized Rascal Triangles are characterized by arithmetic sequences on all diagonals as well as a Rascal-like multiplication and addition rules.