The French Toast Problem

Date: Thu, 5 Feb 2015
From: Vladimir Lifschitz
To: TAG

Over the years, members of TAG have been involved in many interesting
technical discussions.  The transcripts of these discussions are posted
at http://www.cs.utexas.edu/tag/discussions.html.  These days such
discussions became, unfortunately, less frequent, and TAG turned almost
exclusively into a mailing list for announcements.

In an effort to reverse this trend, I'm offering you today a problem to
think about.  If you find it interesting and arrive at a solution,
please send it to me (vl@cs.utexas.edu), but don't broadcast it to the
whole mailing list,  At some point I'll post your solutions online, and
we'll be able to compare different approaches.

The French Toast Problem, described below, is a planning problem, maybe
a little unusual, and the challenge is to arrive at an answer by
describing the domain in an implemented declarative language (for
instance, in the input language of an answer set system).  The
difference between this challenge and what is usually done in ASP
competitions is that efficiency is not an issue in this case, because
the search space is small.  Rather, we are interested in representations
that are elegant and easy to understand.

Here goes:

You have three pieces of uncooked french toast and one hot pan. Each one
needs to be cooked on both sides. Each side can be cooked by placing it
on the hot pan for one minute. The pan can only fit two pieces of french
toast at once, and only one side of each at a time. How many minutes
does it take to cook all three, and how do you do it?

(By the way, the answer to the first question is not 4.)