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<p>Sudoku is a globally popular Japanese puzzle based on a Latin square structure, where each row and column contains every symbol exactly once. Unlike a standard Latin square, a Sudoku grid is further divided into <i>n</i> sub-regions of size <i>a</i> × <i>b</i> (where <i>ab</i> = <i>n</i>, and <i>a</i> may or may not equal <i>b</i>), with each symbol appearing exactly once in each sub-region. In a typical Latin square or row–column design, the primary sources of variation are rows, columns, and treatments. However, in Sudoku-based designs, an additional source of variation arises from these internal sub-regions. Thus, a Sudoku square can be viewed as a special case of a row–column design that includes a fourth factor: the sub-region effect. Importantly, this additional variation can be estimated without increasing the number of experimental plots, making Sudoku-based designs increasingly attractive in statistical experimentation. The objective of this article is to present methods for constructing incomplete block designs—specifically Balanced Incomplete Block Designs (BIBDs) and Partially Balanced Incomplete Block Designs (PBIBDs)—using Sudoku square structures. Several construction methods are developed and illustrated with examples for clarity and practical application.</p>

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Application of Sudoku Square Designs in Agriculture and Construction of Balanced and Partially Balanced Incomplete Block Designs

  • 期刊论文

  • 发表日期：

    2025年6月10日

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  • Prity Maji,
  • Mriganka Saha,
  • Anurup Majumder,
  • Prit Mondal

摘要

Sudoku is a globally popular Japanese puzzle based on a Latin square structure, where each row and column contains every symbol exactly once. Unlike a standard Latin square, a Sudoku grid is further divided into n sub-regions of size a × b (where ab = n, and a may or may not equal b), with each symbol appearing exactly once in each sub-region. In a typical Latin square or row–column design, the primary sources of variation are rows, columns, and treatments. However, in Sudoku-based designs, an additional source of variation arises from these internal sub-regions. Thus, a Sudoku square can be viewed as a special case of a row–column design that includes a fourth factor: the sub-region effect. Importantly, this additional variation can be estimated without increasing the number of experimental plots, making Sudoku-based designs increasingly attractive in statistical experimentation. The objective of this article is to present methods for constructing incomplete block designs—specifically Balanced Incomplete Block Designs (BIBDs) and Partially Balanced Incomplete Block Designs (PBIBDs)—using Sudoku square structures. Several construction methods are developed and illustrated with examples for clarity and practical application.