God's Number for Lunar Lockout
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2020-07-10
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en
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Abstract
Lunar Lockout is a puzzle game, similar to a sliding puzzle. The aim of the game is to
get a particular playing piece to the middle of the board. Completing this goal can be
very easy, but also very di cult. Generally, con gurations that take more moves to solve
are more di cult. So what is the con guration that takes the biggest number of moves
to be optimally solved? We call this number God's number, and it depends on various
parameters, such as the number of pieces on the board.
To nd God's number for di erent choices of parameters, a Java program has been
written for this thesis, comparing three di erent approaches to nding God's number,
namely: naive exhaustive search, backwards exhaustive search, and probabilistic approxi-
mation.
God's number for Lunar Lockout, with the constraints of the commercially released
version, turns out to be 14, and there are 9 di erent con gurations that take that many
moves. If we were to allow larger numbers of pieces, or bigger boards, determining God's
number becomes intractable very quickly. We can try to approximate God's number, but
this similarly becomes intractable or unreliable very quickly.
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Faculteit der Sociale Wetenschappen