Maximum Number of Steps of Topswops on 18 and 19 Cards

TL;DR

This paper reports computational experiments to determine the maximum number of steps in the game Topswops for 18 and 19 cards, using a parallel algorithm, establishing new exact values for these cases.

Contribution

It provides the first known exact values of f(18) and f(19) for Topswops, utilizing a parallelized algorithm based on Knuth's method.

Findings

f(18)=191

f(19)=221

Used parallel algorithm for computation

Abstract

Let $f(n)$ be the maximum number of steps of Topswops on $n$ cards. In this note, we report our computational experiments to determine the values of $f(18)$ and $f(19)$. By applying an algorithm developed by Knuth in a parallel fashion, we conclude that $f(18)=191$ and $f(19)=221$.