{"id":148,"date":"2007-05-08T00:39:04","date_gmt":"2007-05-08T04:39:04","guid":{"rendered":"http:\/\/mat.tepper.cmu.edu\/blog\/?p=137"},"modified":"2007-05-08T00:39:04","modified_gmt":"2007-05-08T04:39:04","slug":"mathematical-puzzles-martin-gardner-and-peter-winkler","status":"publish","type":"post","link":"https:\/\/mat.tepper.cmu.edu\/blog\/index.php\/2007\/05\/08\/mathematical-puzzles-martin-gardner-and-peter-winkler\/","title":{"rendered":"Mathematical Puzzles, Martin Gardner, and Peter Winkler"},"content":{"rendered":"

I am certainly not alone when I say that interest in mathematics was sparked by Martin Gardner’s Mathematical Games<\/a> column in Scientific American<\/em>. I have a strong memory of many boring physics classes in high school which I whiled away reading through the stack of Scientific American<\/em>s in the corner. Those columns led to mathematics in university (where I probably not coincidently received a “D” in physics) and onward through my interest in discrete optimization.<\/p>\n

While Gardner has long since stopped writing the column, his influence remains strong. Every year, a group of mathemeticians, magicians, jugglers, puzzle makers and so on meet at a “Gathering for Gardner<\/a>“, a get-together that looks to be a blast!<\/p>\n

Last year, Peter Winkler<\/a>, formerly of Lucent and now at Darmouth, put together a set of puzzles, cleverly and correctly entitled “7 Puzzles You Think You Must Not Have Heard Correctly”<\/a>. Here is one I particularly like:<\/p>\n

The names of 100 prisoners are placed in 100 wooden boxes, one name to a box, and the boxes are lined up on a table in a room. One by one, the prisoners are led into the room; each may look in at most 50 boxes, but must leave the room exactly as he found it and is permitted no further communication with the others.<\/p>\n

The prisoners have a chance to plot their strategy in advance, and they are going to need it, because unless every single prisoner finds his own name all will subsequently be executed. Find a strategy for them which which has probability of success exceeding 30%. Comment: If each prisoner examines a random set of 50 boxes, their probability of survival is an unenviable 1\/2^100 = 000000000000000000000000000008. They could do worse if they all look in the same 50 boxes, their chances drop to zero. 30% seems ridiculously out of reach but yes, you heard the problem correctly.<\/p><\/blockquote>\n

Is this really possible? Check out Peter’s writeup<\/a> for the solution (and seven other problems). Also check out his book<\/a> for more.<\/p>\n","protected":false},"excerpt":{"rendered":"

I am certainly not alone when I say that interest in mathematics was sparked by Martin Gardner’s Mathematical Games column in Scientific American. I have a strong memory of many boring physics classes in high school which I whiled away reading through the stack of Scientific Americans in the corner. Those columns led to mathematics … Continue reading “Mathematical Puzzles, Martin Gardner, and Peter Winkler”<\/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":[7],"tags":[],"class_list":["post-148","post","type-post","status-publish","format-standard","hentry","category-books"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mat.tepper.cmu.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts\/148","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.tepper.cmu.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.tepper.cmu.edu\/blog\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.tepper.cmu.edu\/blog\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.tepper.cmu.edu\/blog\/index.php\/wp-json\/wp\/v2\/comments?post=148"}],"version-history":[{"count":0,"href":"https:\/\/mat.tepper.cmu.edu\/blog\/index.php\/wp-json\/wp\/v2\/posts\/148\/revisions"}],"wp:attachment":[{"href":"https:\/\/mat.tepper.cmu.edu\/blog\/index.php\/wp-json\/wp\/v2\/media?parent=148"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.tepper.cmu.edu\/blog\/index.php\/wp-json\/wp\/v2\/categories?post=148"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.tepper.cmu.edu\/blog\/index.php\/wp-json\/wp\/v2\/tags?post=148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}