{"id":3837,"date":"2023-08-25T11:04:00","date_gmt":"2023-08-25T15:04:00","guid":{"rendered":"http:\/\/mathfun4kids.com\/mlog\/?p=3837"},"modified":"2024-10-25T09:31:40","modified_gmt":"2024-10-25T13:31:40","slug":"mathcounts-training-number-theory-2","status":"publish","type":"post","link":"https:\/\/mathfun4kids.com\/mlog\/?p=3837","title":{"rendered":"MathCounts Training &#8211; Number Theory &#8211; 2"},"content":{"rendered":"\n<ol><li>________ In base $b$, $441_b$ is equal to $n^2$ in base 10, and $351_b$ is equal to $(n-2)^2$. What is the value of $b$, expressed in base 10?<\/li><li>________ The base-three representation of $0.\\overline{12}$ is equivalent to what base-ten common fraction?<\/li><li> ________ For how many natural numbers less than 100 is the product of the number&#8217;s distinct prime factors equals to 6?<\/li><li>________ A positive number is called $n$-primable if it is divisible by $n$  and each of its digits is a one-digit prime number. How many 3-primable positive integers are then that are less than 1000?<\/li><li>________ Simplify: $$(1\\dfrac{1}{2})^{-2}+(1\\dfrac{1}{2})^{-1}+(1\\dfrac{1}{2})^{0}+(1\\dfrac{1}{2})^{1}+(1\\dfrac{1}{2})^{2}$$<\/li><\/ol>\n","protected":false},"excerpt":{"rendered":"<p>________ In base $b$, $441_b$ is equal to $n^2$ in base 10, and $351_b$ is equal to $(n-2)^2$. What is the value of $b$, expressed in base 10? ________ The base-three representation of $0.\\overline{12}$ is equivalent to what base-ten common &hellip; <a href=\"https:\/\/mathfun4kids.com\/mlog\/?p=3837\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[18,11,16],"tags":[],"_links":{"self":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3837"}],"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=3837"}],"version-history":[{"count":4,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3837\/revisions"}],"predecessor-version":[{"id":3842,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3837\/revisions\/3842"}],"wp:attachment":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3837"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3837"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3837"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}