{"id":4619,"date":"2014-02-18T17:33:22","date_gmt":"2014-02-18T21:33:22","guid":{"rendered":"http:\/\/nycphantom.com\/journal\/?p=4619"},"modified":"2014-02-22T13:58:52","modified_gmt":"2014-02-22T17:58:52","slug":"cuny-math-challenge","status":"publish","type":"post","link":"http:\/\/nycphantom.com\/journal\/?p=4619","title":{"rendered":"CUNY Math Challenge"},"content":{"rendered":"<p>I've registered for <a href=\"http:\/\/math.cisdd.org\/\" target=\"_blank\">4 Rounds<\/a> of fun. Because I also want some money $2,500.<\/p>\n<p>First round questions: (One week left)<\/p>\n<p>Problem 1<br \/>\nHow many di\ufb00erent (non-congruent) triangles have integer side lengths and perimeter 2014?<\/p>\n<p><span style=\"color: #ff0000;\"><a href=\"http:\/\/mathworld.wolfram.com\/AlcuinsSequence.html\" target=\"_blank\"><span style=\"color: #ff0000;\">Alcuin's Sequence<\/span><\/a> is the hint. A <a href=\"http:\/\/www.jstor.org\/stable\/2690701\" target=\"_blank\"><span style=\"color: #ff0000;\">detailed <\/span><\/a>explanation. Thanks to <a href=\"http:\/\/math.stackexchange.com\/questions\/170319\/how-many-triangles-with-integral-side-lengths-are-possible-provided-their-perim\" target=\"_blank\"><span style=\"color: #ff0000;\">JM<\/span><\/a>.<\/span><br \/>\nProblem 2<br \/>\nYou have 2014 identical looking coins and a two-pan balance scale with no weights. One of the coins is\u00a0fake, but you do not know whether it is lighter or heavier than the genuine coins, which all weigh the same.<br \/>\nDescribe a procedure to determine in the minimum number of weighings whether the fake coin is lighter or\u00a0heavier than the others.<\/p>\n<p><span style=\"color: #ff0000;\">Pile them in 3s or 2s.<\/span><span style=\"color: #ff0000;\"> Looks like all these can be googled.<\/span><br \/>\nProblem 3<br \/>\nA fair coin is tossed repeatedly until 3 heads appear consecutively. On average, how many times is it tossed?<\/p>\n<p><span style=\"color: #ff0000;\">This is kindergarten level.<\/span><br \/>\nProblem 4<br \/>\nThere are four knights on a 3 3 chessboard: two white knights at the bottom two corners, and two black\u00a0knights at the two upper corners. Show how to switch the knights in the minimum number of moves so\u00a0that the white knights are at the upper corners and the black knights are the bottom corners. (Knights\u00a0cannot land on each others squares during this process.)<\/p>\n<p><span style=\"color: #ff0000;\">I need a board. But this is <a href=\"http:\/\/press.princeton.edu\/chapters\/s7714.html\" target=\"_blank\">supposed <\/a>to have been <a href=\"http:\/\/www.chess.com\/forum\/view\/more-puzzles\/guarinis-problem\" target=\"_blank\">solved<\/a>: <a href=\"http:\/\/www.ams.org\/bookstore\/pspdf\/mbk-63-prev.pdf\" target=\"_blank\">Guarini's Problem<\/a><br \/>\n<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I've registered for 4 Rounds of fun. Because I also want some money $2,500. First round questions: (One week left) Problem 1 How many di\ufb00erent (non-congruent) triangles have integer side lengths and perimeter 2014? Alcuin's Sequence is the hint. A &hellip; <a href=\"http:\/\/nycphantom.com\/journal\/?p=4619\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[27],"tags":[],"class_list":["post-4619","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"_links":{"self":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts\/4619","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4619"}],"version-history":[{"count":6,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts\/4619\/revisions"}],"predecessor-version":[{"id":4651,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts\/4619\/revisions\/4651"}],"wp:attachment":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4619"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4619"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4619"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}