{"id":2186,"date":"2021-08-17T19:48:20","date_gmt":"2021-08-17T19:48:20","guid":{"rendered":"http:\/\/mathfun4kids.com\/mlog\/?p=2186"},"modified":"2021-08-17T19:50:59","modified_gmt":"2021-08-17T19:50:59","slug":"fun-math-puzzles-1","status":"publish","type":"post","link":"https:\/\/mathfun4kids.com\/mlog\/?p=2186","title":{"rendered":"Fun Math Puzzles &#8211; 1"},"content":{"rendered":"\n<p>My calculator is broken, it only has two working buttons. One of them adds $1$ to the result and the other doubles it. What is the minimum number of presses needed to get to 2021?<\/p>\n\n<button onclick=\"toggle_visibility(&quot;solution&quot;)\">Click for the solution<\/button>\n\n<div style=\"display:none\" id=\"solution\">We can try to work backwards from 2021. We can start with subtracting 1 to get 2020. Dividing by 2 twice gives 505. We must subtract 1 to get 504. Since 504 is divisible by 8, we can divide 3 times to get 63. Subtracting 1 gives 62. The rest is quite trivial: $$62\\rightarrow 31 \\rightarrow 30 \\rightarrow 15 \\rightarrow 14 \\rightarrow 7 \\rightarrow 6 \\rightarrow 3 \\rightarrow 2 \\rightarrow 1$$ Counting the steps, we have $\\boxed{17}$ as our answer.<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>My calculator is broken, it only has two working buttons. One of them adds $1$ to the result and the other doubles it. What is the minimum number of presses needed to get to 2021? Click for the solution We &hellip; <a href=\"https:\/\/mathfun4kids.com\/mlog\/?p=2186\">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":[6],"tags":[],"_links":{"self":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/2186"}],"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=2186"}],"version-history":[{"count":10,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/2186\/revisions"}],"predecessor-version":[{"id":2196,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/2186\/revisions\/2196"}],"wp:attachment":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2186"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2186"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}