{"id":1983,"date":"2008-10-14T13:32:56","date_gmt":"2008-10-14T18:32:56","guid":{"rendered":"http:\/\/www.allyngibson.net\/?p=1983"},"modified":"2008-10-14T13:32:56","modified_gmt":"2008-10-14T18:32:56","slug":"on-the-morning-brain-teaser","status":"publish","type":"post","link":"http:\/\/www.allyngibson.com\/?p=1983","title":{"rendered":"On the Morning Brain Teaser"},"content":{"rendered":"

We have brain teasers e-mailed to us at work now.<\/p>\n

This morning’s question?<\/p>\n

A certain number consists of two digits. The number is equal to five times the sum of its digits. If you add 9 to the number, the order of its digits is reversed. What is the number?<\/p><\/blockquote>\n

\nHow do we solve this?<\/p>\n

Define two variables: a<\/i> and b<\/i>. The two digit number would be 10a<\/i>+b.<\/p>\n

Consider the first sentence. “The number is equal to five times the sum of its two digits.”<\/p>\n

10a<\/i>+b<\/i>=5(a<\/i>+b<\/i>)<\/p>\n

Now we solve for a<\/i>.<\/p>\n

10a<\/i>+b<\/i>=5a<\/i>+5b<\/i>
\n5a<\/i>=4b<\/i>
\na<\/i>=4b<\/i>\/5<\/p>\n

Consider the second sentence. “If you add 9 to the number, the order of its digits are reversed.”<\/p>\n

10a<\/i>+b<\/i>+9=10b<\/i>+a<\/i><\/p>\n

Now we solve for a<\/i>.<\/p>\n

9a<\/i>=9b<\/i>-9
\na<\/i>=b<\/i>-1<\/p>\n

Now, we combine the two.<\/p>\n

b<\/i>-1=4b<\/i>\/5
\n5b<\/i>-5=4b<\/i>
\nb<\/i>=5<\/p>\n

Now, we plug b<\/i> into one of our solutions for a<\/i>.<\/p>\n

a<\/i>=b<\/i>-1
\na<\/i>=5-1
\na<\/i>=4<\/p>\n

Thus, our solution for the number?<\/p>\n

10a<\/i>+b<\/i>
\n10*4+5
\n40+5
\n45<\/p>\n

And there’s our solution. The two digit number is 45.<\/p>\n

Add the two digits, and you get 9. Multiply that by 5, and you get 45.<\/p>\n

Reverse the digits and you get 54, which is the number — 45 — plus 9.<\/p>\n

Elementary! \ud83d\ude42<\/p>\n","protected":false},"excerpt":{"rendered":"

We have brain teasers e-mailed to us at work now. This morning’s question? A certain number consists of two digits. The number is equal to five times the sum of its digits. If you add 9 to the number, the order of its digits is reversed. What is the number? How do we solve this?Continue reading “On the Morning Brain Teaser”<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[114],"tags":[],"class_list":["post-1983","post","type-post","status-publish","format-standard","hentry","category-asides","entry"],"_links":{"self":[{"href":"http:\/\/www.allyngibson.com\/index.php?rest_route=\/wp\/v2\/posts\/1983","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.allyngibson.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.allyngibson.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.allyngibson.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/www.allyngibson.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1983"}],"version-history":[{"count":0,"href":"http:\/\/www.allyngibson.com\/index.php?rest_route=\/wp\/v2\/posts\/1983\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.allyngibson.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1983"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.allyngibson.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1983"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.allyngibson.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1983"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}