This work is licensed under a Creative Commons Attribution 4.0 International License. Probably the first appearance of the 3-fractions puzzle in the constraints literature is [schulte2004finite].
The following paper shows how a basic model of the 3-fractions puzzle can be improved automatically [frisch2001extensions].
Using hand-reformulation, the following paper discusses how different using symmetry-breaking schemes on the 3-fractions puzzle, followed by the derivation of implied constraints, can lead to models of varying quality [frisch2004symmetry].
The following paper investigates the numerical issues arising when the number of fractions grows and two new CP models that exploit the integer factorization of the fractions’ denominators [malapert2017puzzle].
The note [codish2018sat] describes a SAT encoding for the n-fractions puzzle for which a SAT solver found new solutions for some of the remaining open instances of this problem.
Only the 44-fractions remains open when combining the most recent results of [malapert2017puzzle] and [codish2018sat]. Other n-fractions have been found or proven infeasible.
[codish2018sat]
A SAT Encoding for the n-Fractions Problem
CoRR,
2018
[schulte2004finite]
Finite Domain Constraint Programming in Oz. A Tutorial.
Available at www. mozart-oz. org,
2004
[frisch2004symmetry]
Symmetry breaking as a prelude to implied constraints: A constraint modelling pattern
ECAI, 171,
2004
[frisch2001extensions]
Extensions to proof planning for generating implied constraints
In Proceedings of Calculemus-01,
2001
[malapert2017puzzle]
Puzzle—Solving the n-Fractions Puzzle as a Constraint Programming Problem
null,
0
This work is licensed under a Creative Commons Attribution 4.0 International License.