{"id":6659,"date":"2018-08-03T09:34:26","date_gmt":"2018-08-03T13:34:26","guid":{"rendered":"http:\/\/www.decisionsciencenews.com\/?p=6659"},"modified":"2018-08-03T09:40:32","modified_gmt":"2018-08-03T13:40:32","slug":"the-18-cent-piece","status":"publish","type":"post","link":"https:\/\/www.decisionsciencenews.com\/?p=6659","title":{"rendered":"The 18 cent piece"},"content":{"rendered":"<p>WHAT SET OF COINS MINIMIZES THE AVERAGE NUMBER OF COINS NEEDED TO MAKE CHANGE?<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/coin-18.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-6669\" src=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/coin-18.png\" alt=\"\" width=\"484\" height=\"333\" srcset=\"https:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/coin-18.png 484w, https:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/coin-18-300x206.png 300w\" sizes=\"auto, (max-width: 484px) 100vw, 484px\" \/><\/a><\/p>\n<p>We draw your attention to the cleverly-titled article <a href=\"https:\/\/cs.uwaterloo.ca\/~shallit\/Papers\/change2.pdf\">What This Country Needs is an 18 Cent Piece<\/a>. It&#8217;s a piece of recreational mathematics that asks the question &#8220;what set of coins minimizes the average number of coins needed to make change&#8221;?<\/p>\n<p>It&#8217;s fun, but I&#8217;m sure my marketing colleagues will bristle at the assumption &#8220;we assume that every amount of change between 0 and 99 is equally likely.&#8221; That said, the author does acknowledge <a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0165176597000098\">nines pricing<\/a> and <a href=\"http:\/\/www.decisionsciencenews.com\/2011\/10\/05\/do-cents-follow-benfords-law\/\">Benford&#8217;s law<\/a> in a footnote.<\/p>\n<p>We also imagine this to be the kind of article that when dangled before our serial co-author <a href=\"https:\/\/en.wikipedia.org\/wiki\/Preston_McAfee\">Preston McAfee<\/a>, would cause him to engage in a few hours of recreational mathematics himself.<\/p>\n<p>CITATION<br \/>\nShallit, J. The Mathematical Intelligencer (2003) 25: 20. https:\/\/doi.org\/10.1007\/BF02984830<\/p>\n","protected":false},"excerpt":{"rendered":"<p>WHAT SET OF COINS MINIMIZES THE AVERAGE NUMBER OF COINS NEEDED TO MAKE CHANGE? We draw your attention to the cleverly-titled article What This Country Needs is an 18 Cent Piece. It&#8217;s a piece of recreational mathematics that asks the question &#8220;what set of coins minimizes the average number of coins needed to make change&#8221;? [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[4,16],"tags":[1753,1759,1755,1131,475,953,1754,1760,67,625,1752,1757,1735,1758,1756],"class_list":["post-6659","post","type-post","status-publish","format-standard","hentry","category-encyclopedia","category-ideas","tag-1753","tag-benfords","tag-cent","tag-change","tag-coins","tag-country","tag-eighteen","tag-law","tag-marketing","tag-mathematics","tag-needs","tag-nines","tag-piece","tag-pricing","tag-recreational"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4LKj-1Jp","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts\/6659","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6659"}],"version-history":[{"count":4,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts\/6659\/revisions"}],"predecessor-version":[{"id":6672,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts\/6659\/revisions\/6672"}],"wp:attachment":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6659"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6659"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6659"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}