{"id":64,"date":"2020-01-05T23:51:47","date_gmt":"2020-01-05T23:51:47","guid":{"rendered":"http:\/\/mathfun4kids.com\/mlog\/?p=64"},"modified":"2020-10-16T20:18:25","modified_gmt":"2020-10-16T20:18:25","slug":"mathcounts-exercises-9","status":"publish","type":"post","link":"https:\/\/mathfun4kids.com\/mlog\/?p=64","title":{"rendered":"MATHCOUNTS Exercises \u2013 9"},"content":{"rendered":"\n<p>A unit cube is painted with 1 face in red, 1 face in green, 1 face in yellow, and 3 faces in blue color. How many unique ways to paint the cube? <a href=\"javascript:toggle_visibility('sol-mathcounts-exercises-9');\">Click here for the solution.<\/a><\/p>\n\n\n\n<div id=\"sol-mathcounts-exercises-9\" style=\"display:none\">\n<p><strong>Solution<\/strong> There are only 2 ways to paint 3 faces in blue color, as shown below with unfold cube faces:<\/p>\n<img width=\"322\" src=\"wp-content\/uploads\/2020\/10\/Screen-Shot-2019-12-27-at-5.16.16-PM.png\" alt=\"\" class=\"wp-image-65\" srcset=\"https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2019-12-27-at-5.16.16-PM.png 966w, https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2019-12-27-at-5.16.16-PM-300x105.png 300w, https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2019-12-27-at-5.16.16-PM-768x269.png 768w\" sizes=\"(max-width: 966px) 100vw, 966px\" \/> \n<p>For the first case where 3 blue faces form a strip, there are 3 ways to paint the remaining 3 faces, by painting the face opposite to the middle blue face in red, green, or yellow, as shown below, with the center blue face not displayed.\n<\/p>\n<img width=\"363\" src=\"wp-content\/uploads\/2020\/10\/Screen-Shot-2019-12-27-at-11.59.35-PM.png\" alt=\"\" class=\"wp-image-69\" srcset=\"https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2019-12-27-at-11.59.35-PM.png 726w, https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2019-12-27-at-11.59.35-PM-300x102.png 300w\" sizes=\"(max-width: 726px) 100vw, 726px\" \/>\n<p>For the second case where 3 blue faces jointing at a corner, there are 2 ways to paint the remaining 3 faces, either in clockwise order or in counter-clockwise order, as shown below with the 3 blue faces hiding in the back.<\/p>\n<img width=\"224\" src=\"wp-content\/uploads\/2020\/10\/Screen-Shot-2019-12-27-at-11.59.49-PM.png\" alt=\"\" class=\"wp-image-73\" srcset=\"https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2019-12-27-at-11.59.49-PM.png 448w, https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2019-12-27-at-11.59.49-PM-300x141.png 300w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/>\n<p>Therefore, there are 5 unique ways to paint the cube, as show below with unfold faces:<\/p> \n<img width=\"384\" src=\"wp-content\/uploads\/2020\/10\/Screen-Shot-2019-12-27-at-10.30.43-PM.png\" alt=\"\" class=\"wp-image-75\" srcset=\"https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2019-12-27-at-10.30.43-PM.png 768w, https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2019-12-27-at-10.30.43-PM-300x163.png 300w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>A unit cube is painted with 1 face in red, 1 face in green, 1 face in yellow, and 3 faces in blue color. How many unique ways to paint the cube? Click here for the solution. Solution There are &hellip; <a href=\"https:\/\/mathfun4kids.com\/mlog\/?p=64\">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":{"inline_featured_image":false},"categories":[10,9,11],"tags":[],"_links":{"self":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/64"}],"collection":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=64"}],"version-history":[{"count":17,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/64\/revisions"}],"predecessor-version":[{"id":565,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/64\/revisions\/565"}],"wp:attachment":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=64"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=64"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=64"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}