Nearly magic rectangles

Feng Shun Chai, Rakhi Singh, John Stufken

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Magic squares have been extremely useful and popular in combinatorics and statistics. One generalization of magic squares is magic rectangles which are useful for designing experiments in statistics. A necessary and sufficient condition for the existence of magic rectangles restricts the number of rows and columns to be either both odd or both even. In this paper, we generalize magic rectangles to even by odd nearly magic rectangles. We also prove necessary and sufficient conditions for the existence of a nearly magic rectangle, and construct one for each parameter set for which they exist.

Original languageEnglish (US)
Pages (from-to)562-567
Number of pages6
JournalJournal of Combinatorial Designs
Issue number9
StatePublished - Sep 2019
Externally publishedYes


  • magic rectangle
  • magic square
  • row-column design

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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