Preprint Open Access

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

Inder J. Taneja

MARC21 XML Export

<?xml version='1.0' encoding='UTF-8'?>
<record xmlns="">
  <datafield tag="041" ind1=" " ind2=" ">
    <subfield code="a">eng</subfield>
  <datafield tag="653" ind1=" " ind2=" ">
    <subfield code="a">Magic Squares, Block-Wise Magic Squares, Equal Sum Sub-Blocks, Unequal Sum Sub-Blocks</subfield>
  <controlfield tag="005">20200120161959.0</controlfield>
  <controlfield tag="001">2555343</controlfield>
  <datafield tag="856" ind1="4" ind2=" ">
    <subfield code="s">5566406</subfield>
    <subfield code="z">md5:050dc6ead5e8bcfbf5b4c650b99e2f07</subfield>
    <subfield code="u"></subfield>
  <datafield tag="542" ind1=" " ind2=" ">
    <subfield code="l">open</subfield>
  <datafield tag="260" ind1=" " ind2=" ">
    <subfield code="c">2019-02-01</subfield>
  <datafield tag="909" ind1="C" ind2="O">
    <subfield code="p">openaire</subfield>
    <subfield code="o"></subfield>
  <datafield tag="100" ind1=" " ind2=" ">
    <subfield code="u">Formerly, Professor of Mathematics, Universidade Federal de Santa Catarina, Florianópolis, SC, Brazil</subfield>
    <subfield code="a">Inder J. Taneja</subfield>
  <datafield tag="245" ind1=" " ind2=" ">
    <subfield code="a">Block-Wise Magic and Bimagic Squares of Orders 12 to 36</subfield>
  <datafield tag="540" ind1=" " ind2=" ">
    <subfield code="u"></subfield>
    <subfield code="a">Creative Commons Attribution 4.0 International</subfield>
  <datafield tag="650" ind1="1" ind2="7">
    <subfield code="a">cc-by</subfield>
    <subfield code="2"></subfield>
  <datafield tag="520" ind1=" " ind2=" ">
    <subfield code="a">&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;</subfield>
  <datafield tag="773" ind1=" " ind2=" ">
    <subfield code="n">doi</subfield>
    <subfield code="i">isVersionOf</subfield>
    <subfield code="a">10.5281/zenodo.2555342</subfield>
  <datafield tag="024" ind1=" " ind2=" ">
    <subfield code="a">10.5281/zenodo.2555343</subfield>
    <subfield code="2">doi</subfield>
  <datafield tag="980" ind1=" " ind2=" ">
    <subfield code="a">publication</subfield>
    <subfield code="b">preprint</subfield>
All versions This version
Views 264263
Downloads 8989
Data volume 495.4 MB495.4 MB
Unique views 244243
Unique downloads 7373


Cite as