Partitioning the $5\times 5$ array into restrictions of circles
DOI:
https://doi.org/10.11575/cdm.v15i1.62808Abstract
We show that there is a unique way to partition a $5\times 5$ array of lattice points into restrictions of five circles. This result is extended to the $6\times 5$ array, and used to show the optimality of a six-circle solution for the $6\times 6$ array.
References
S. Chow, Solution to Problem CC266, Crux Mathematicorum {\bf 44(3)} (2018), 137
R. Honsberger, Problem CC266, Crux Mathematicorum {\bf 43(4)}(2017), 124--125
E. Landau, {\"U}ber die Einteilung der positiven ganzen Zahlen in vier Klassen nach der Mindeszahl der zu ihrer additiven Zusammensetzung erforderlichen Quadrate, {\em Arch. Math. Phys.} {\bf 13} (1908), 305--312.
J. G. MacLauchlin, comment, Crux Mathematicorum {\bf 44(3)} (2018), 137
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