In How Ways Can You Play Stanley Solitaire?

TL;DR

This paper introduces Stanley Solitaire, a simple game, and provides a closed-form formula for counting its possible plays, relying on a deep existing theorem, and invites readers to find a more elementary proof.

Contribution

It presents the first explicit formula for the number of ways to play Stanley Solitaire, connecting it to Richard Stanley's 1984 theorem.

Findings

Closed-form formula for Stanley Solitaire

Connection to Richard Stanley's theorem

Invitation for elementary proof

Abstract

We introduce a very simple solitaire game, named Stanley Solitaire, in honor of Richard Stanley, and prove an explicit closed-form formula for the number of ways of playing it. Alas, the only proof that we know is via a deep theorem of Richard Stanley from 1984. We challenge the readers to find a more elementary proof.