{"id":118,"date":"2008-06-17T10:26:49","date_gmt":"2008-06-17T09:26:49","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=118"},"modified":"2008-06-17T10:26:49","modified_gmt":"2008-06-17T09:26:49","slug":"puzzle-express-2008-with-a-minimal-number-of-just-one-digit","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=118","title":{"rendered":"Puzzle: Express 2008 with a minimal number of just one digit."},"content":{"rendered":"<p>At the beginning of the year I wondered what <a href=\"https:\/\/www.walkingrandomly.com\/?p=40\">interesting facts I could discover about the number 2008<\/a> and, with the help of readers of this blog, I came up with a lot more than I expected to.  Now that we are over half way through the year I thought it was time to take another look at the integer 2008 with the following puzzle.<\/p>\n<p>Choose any one of the digits from 0 to 9 and attempt to express the number 2008 using only that digit.  You can repeat your digit as often as you like and use any of functions that are built into something like <a href=\"http:\/\/www.wolfram.com\/\">Mathematica<\/a>, <a href=\"http:\/\/www.mathworks.com\/\">MATLAB<\/a> or <a href=\"http:\/\/www.sagemath.org\/\">SAGE<\/a> but, as you may expect, kudos will be awarded for using only simple functions and small numbers of repeats.<\/p>\n<p>I spent a few minutes thinking about this problem and so far have only come up with<\/p>\n<p>2008=  (2*2^2)*(2^2^2)^2 &#8211; 2*2^(2*2) &#8211; 2*(2 + 2)<\/p>\n<p>2008 = Ceiling[6*6*6*6 + 6! &#8211; Sqrt[66]]<\/p>\n<p>2008 = Ceiling[Gamma[7.7] &#8211; (777) + 7 + 7 + 7\/7]<\/p>\n<p>but I am sure you can do better &#8211; those ceiling functions are pretty ugly for a start.  Feel free to post your solutions in the comments section &#8211; I look forward to seeing them.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>At the beginning of the year I wondered what interesting facts I could discover about the number 2008 and, with the help of readers of this blog, I came up with a lot more than I expected to. Now that we are over half way through the year I thought it was time to take [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[13,6],"tags":[],"class_list":["post-118","post","type-post","status-publish","format-standard","hentry","category-games","category-general-math"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3swhs-1U","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/118","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=118"}],"version-history":[{"count":0,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/118\/revisions"}],"wp:attachment":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=118"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=118"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}