Preprint Open Access

Block-Wise Magic and Bimagic Squares of Orders 12 to 36

Inder J. Taneja


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  <identifier identifierType="DOI">10.5281/zenodo.2555343</identifier>
  <creators>
    <creator>
      <creatorName>Inder J. Taneja</creatorName>
      <affiliation>Formerly, Professor of Mathematics, Universidade Federal de Santa Catarina, Florianópolis, SC, Brazil</affiliation>
    </creator>
  </creators>
  <titles>
    <title>Block-Wise Magic and Bimagic Squares of Orders 12 to 36</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2019</publicationYear>
  <subjects>
    <subject>Magic Squares, Block-Wise Magic Squares, Equal Sum Sub-Blocks, Unequal Sum Sub-Blocks</subject>
  </subjects>
  <dates>
    <date dateType="Issued">2019-02-01</date>
  </dates>
  <language>en</language>
  <resourceType resourceTypeGeneral="Preprint"/>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/2555343</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.2555342</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="https://creativecommons.org/licenses/by/4.0/legalcode">Creative Commons Attribution 4.0 International</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&lt;p&gt;This paper summarize some of the results done before by author on &lt;strong&gt;block-wise constructions&amp;nbsp;of magic squares&lt;/strong&gt;. &amp;nbsp;In this paper, we shall rewrite some these results without details. The details can be seen in the reference list. This is done for the magic squares of orders 12 to 36, i.e., for the orders 12, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 33, 35 and 36. In some cases, the magic squares are &lt;strong&gt;bimagic&lt;/strong&gt;&amp;nbsp;or &lt;strong&gt;semi-bimagic&lt;/strong&gt;. We tried to bring all the possible combinations in each case.&amp;nbsp;In all the cases, at least one of the &lt;strong&gt;block-wise representation&lt;/strong&gt;&amp;nbsp;is &lt;strong&gt;pandiagonal&lt;/strong&gt;&amp;nbsp;except the orders 18 and 30. Magic squares for the prime numbers and double of prime numbers, such as, 11, 13, 22, 26, etc. are not considered.&amp;nbsp;&lt;/p&gt;</description>
  </descriptions>
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