{"id":17,"date":"2007-09-30T02:45:35","date_gmt":"2007-09-30T02:45:35","guid":{"rendered":"http:\/\/sschinder.wordpress.com\/2007\/09\/30\/making-odd-size-magic-squares"},"modified":"2019-11-21T10:19:09","modified_gmt":"2019-11-21T02:19:09","slug":"making-odd-size-magic-squares","status":"publish","type":"post","link":"https:\/\/squarez.motd.org\/?p=17","title":{"rendered":"Making odd size magic squares"},"content":{"rendered":"\n<p>This is one basic technique that can be used to make magic squares whose side length is odd: 3, 5, 7, 9, &#8230;<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Draw the table.<\/li><li>Put the number 1 below the center cell.<\/li><li>Put the next numbers to the right on the row below, wrapping around when necessary.<\/li><li>When the next cell is already filled, put the next number two rows below, wrapping around when necessary.<\/li><\/ol>\n\n\n\n<p>So&nbsp;to make&nbsp;a 3 by 3 square, the first step is to draw the table and put the number 1 under the center cell.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"227\" height=\"228\" src=\"https:\/\/squarez.motd.org\/wp-content\/uploads\/2018\/12\/Sq3x3_1.gif\" alt=\"\" class=\"wp-image-556\"\/><\/figure><\/div>\n\n\n\n<p>\n\nThen put the number 2 to the right and below number 1. Number 2 ends up in the upper right cell, as it is necessary to wrap around when the move exceeds the last row of the table. Accordingly, number 3 ends in the middle left cell, after wrapping around when the move exceeds the right column of the table.\n\n<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"227\" height=\"228\" src=\"https:\/\/squarez.motd.org\/wp-content\/uploads\/2018\/12\/Sq3x3_2.gif\" alt=\"\" class=\"wp-image-557\"\/><\/figure><\/div>\n\n\n\n<p> As the cell to the right and below number 3 is already filled by number 1, number 4 ends two rows below number 3. With the wrap around, this means the upper left cell of the table. <\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"227\" height=\"227\" src=\"https:\/\/squarez.motd.org\/wp-content\/uploads\/2018\/12\/Sq3x3_3.gif\" alt=\"\" class=\"wp-image-558\"\/><\/figure><\/div>\n\n\n\n<p> From then we can resume the below-right move, with one more transition by the 2-rows-below move when the next cell below-right number 6 is already filled by number 4. <\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"227\" height=\"227\" src=\"https:\/\/squarez.motd.org\/wp-content\/uploads\/2018\/12\/Sq3x3_4.gif\" alt=\"\" class=\"wp-image-559\"\/><\/figure><\/div>\n\n\n\n<p>\n\nWhen all the cells are filled, the result is a 3 by 3 magic square. The sums of the numbers in each row, each column and each diagonal are all equal to 15.\n\n<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"227\" height=\"229\" src=\"https:\/\/squarez.motd.org\/wp-content\/uploads\/2018\/12\/Sq3x3_5.gif\" alt=\"\" class=\"wp-image-555\"\/><\/figure><\/div>\n","protected":false},"excerpt":{"rendered":"<p>This is one basic technique that can be used to make magic squares whose side length is odd: 3, 5, 7, 9, &#8230; Draw the table. Put the number 1 below the center cell. Put the next numbers to the &hellip; <a href=\"https:\/\/squarez.motd.org\/?p=17\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-17","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/squarez.motd.org\/index.php?rest_route=\/wp\/v2\/posts\/17","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/squarez.motd.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/squarez.motd.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/squarez.motd.org\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/squarez.motd.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=17"}],"version-history":[{"count":2,"href":"https:\/\/squarez.motd.org\/index.php?rest_route=\/wp\/v2\/posts\/17\/revisions"}],"predecessor-version":[{"id":668,"href":"https:\/\/squarez.motd.org\/index.php?rest_route=\/wp\/v2\/posts\/17\/revisions\/668"}],"wp:attachment":[{"href":"https:\/\/squarez.motd.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=17"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/squarez.motd.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=17"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/squarez.motd.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=17"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}