{"id":505,"date":"2012-08-17T22:57:36","date_gmt":"2012-08-17T14:57:36","guid":{"rendered":"http:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/?p=505"},"modified":"2024-02-16T21:13:18","modified_gmt":"2024-02-16T13:13:18","slug":"apple-cutting-puzzle","status":"publish","type":"post","link":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/2012\/08\/apple-cutting-puzzle\/","title":{"rendered":"Apple Cutting Puzzle"},"content":{"rendered":"

When I cut an apple for my kids, I normally cut it into 6 pieces. I give the biggest piece to my younger son, since he insists on only eating one piece, but I want him to eat more apple.
\n
\nI take the three smallest pieces for myself, and my elder son takes the middle two pieces. <\/p>\n

\"20120817-224837.jpg\"<\/a><\/p>\n

Of course, this means I get the most apple, but it doesn’t have to be that way. I could make sure we all got the same amount by cutting three pieces equal to 1\/9 of the apple each, two equal to 1\/6 each, and the last piece would be 1\/3 of the apple. <\/p>\n

I’ve noticed, by the way, that my local pizza shop never cuts the pizza into equal slices. Do they know that some people want a bigger slice?<\/p>\n

But what if I just cut that apple randomly?<\/p>\n

Today’s puzzle is this. Suppose I divide an apple (or pie, or pizza) into six pieces, by making six straight cuts from the middle in random directions. Then I distribute the pieces as I described above. What’s the chance that the three smallest pieces are less than the biggest piece? Or less than the other two pieces?<\/p>\n

You might want to start with an easier puzzle – if I cut the apple into just three randomly sized pieces, what’s the chance that the largest piece is more than the other two combined?<\/p>\n

Think about this next time you’re cutting an apple…<\/p>\n","protected":false},"excerpt":{"rendered":"

When I cut an apple for my kids, I normally cut it into 6 pieces. I give the biggest piece to my younger son, since he insists on only eating one piece, but I want him to eat more apple.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[392,108,7],"_links":{"self":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts\/505"}],"collection":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/comments?post=505"}],"version-history":[{"count":2,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts\/505\/revisions"}],"predecessor-version":[{"id":1337,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts\/505\/revisions\/1337"}],"wp:attachment":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/media?parent=505"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/categories?post=505"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/tags?post=505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}