Move Project Euler under puzzles.
This commit is contained in:
91
puzzles/project_euler/pe/p343.html
Normal file
91
puzzles/project_euler/pe/p343.html
Normal file
@@ -0,0 +1,91 @@
|
||||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<meta charset="utf-8" />
|
||||
<meta name="author" content="Colin Hughes" />
|
||||
<meta name="description" content="A website dedicated to the fascinating world of mathematics and programming" />
|
||||
<meta name="keywords" content="programming,mathematics,problems,puzzles" />
|
||||
|
||||
<title>Problem 343 - Project Euler</title>
|
||||
<link rel="shortcut icon" href="http://projecteuler.net/favicon.ico" />
|
||||
<link rel="stylesheet" type="text/css" href="style_main.css" />
|
||||
<link rel="stylesheet" type="text/css" href="style_light.css" />
|
||||
<script type="text/x-mathjax-config">
|
||||
MathJax.Hub.Config({
|
||||
jax: ["input/TeX", "output/HTML-CSS"],
|
||||
tex2jax: {
|
||||
inlineMath: [ ["$","$"], ["\\(","\\)"] ],
|
||||
displayMath: [ ["$$","$$"], ["\\[","\\]"] ],
|
||||
processEscapes: true
|
||||
},
|
||||
"HTML-CSS": { availableFonts: ["TeX"] }
|
||||
});
|
||||
</script>
|
||||
|
||||
<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML">
|
||||
</script>
|
||||
</head>
|
||||
|
||||
<body>
|
||||
<div id="container">
|
||||
|
||||
<div id="nav" class="noprint">
|
||||
<ul>
|
||||
<li><a href="about" title="About" accesskey="h">About</a></li>
|
||||
<li><a href="register" title="Register" accesskey="1">Register</a></li>
|
||||
<li id="current"><a href="problems" title="Problems" accesskey="2">Problems</a></li>
|
||||
<li><a href="login" title="Login" accesskey="3">Login</a></li>
|
||||
</ul>
|
||||
</div>
|
||||
<div id="info_panel"><a href="rss2_euler.xml"><img src="images/icon_rss.png" alt="RSS Feed" title="RSS Feed" /></a><a href="secure=57be2"><img src="images/icon_lock.png" alt="Use secure connection" title="Use secure connection" /></a></div>
|
||||
|
||||
<div id="logo" class="noprint">
|
||||
<img src="images/pe_banner_light.png" alt="Project Euler .net" />
|
||||
</div>
|
||||
|
||||
<div id="content">
|
||||
<div style="text-align:center;" class="print"><img src="images/pe_banner.png" alt="projecteuler.net" style="border:none;" /></div>
|
||||
<h2>Fractional Sequences</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 343</h3><span style="width:300px;color:#666;">Published on Saturday, 18th June 2011, 04:00 pm; Solved by 736</span></div>
|
||||
<div class="problem_content" role="problem">
|
||||
<p>For any positive integer <var>k</var>, a finite sequence a<sub><var>i</var></sub> of fractions x<sub><var>i</var></sub>/y<sub><var>i</var></sub> is defined by:<br />
|
||||
a<sub>1</sub> = 1/<var>k</var> and<br />
|
||||
a<sub><var>i</var></sub> = (x<sub><var>i</var>-1</sub>+1)/(y<sub><var>i</var>-1</sub>-1) reduced to lowest terms for <var>i</var>>1.<br />
|
||||
When a<sub><var>i</var></sub> reaches some integer <var>n</var>, the sequence stops. (That is, when y<sub><var>i</var></sub>=1.)<br />
|
||||
Define f(<var>k</var>) = <var>n</var>. <br />
|
||||
For example, for <var>k</var> = 20:
|
||||
</p>
|
||||
|
||||
<p>
|
||||
1/20 <img src='images/symbol_maps.gif' width='15' height='7' alt='→' border='0' style='vertical-align:middle;' /> 2/19 <img src='images/symbol_maps.gif' width='15' height='7' alt='→' border='0' style='vertical-align:middle;' /> 3/18 = 1/6 <img src='images/symbol_maps.gif' width='15' height='7' alt='→' border='0' style='vertical-align:middle;' /> 2/5 <img src='images/symbol_maps.gif' width='15' height='7' alt='→' border='0' style='vertical-align:middle;' /> 3/4 <img src='images/symbol_maps.gif' width='15' height='7' alt='→' border='0' style='vertical-align:middle;' /> 4/3 <img src='images/symbol_maps.gif' width='15' height='7' alt='→' border='0' style='vertical-align:middle;' /> 5/2 <img src='images/symbol_maps.gif' width='15' height='7' alt='→' border='0' style='vertical-align:middle;' /> 6/1 = 6
|
||||
</p>
|
||||
|
||||
<p>
|
||||
So f(20) = 6.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Also f(1) = 1, f(2) = 2, f(3) = 1 and Σf(<var>k</var><sup>3</sup>) = 118937 for 1 <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> <var>k</var> <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> 100.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Find Σf(<var>k</var><sup>3</sup>) for 1 <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> <var>k</var> <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> 2<img src='images/symbol_times.gif' width='9' height='9' alt='×' border='0' style='vertical-align:middle;' />10<sup>6</sup>.
|
||||
</p>
|
||||
</div><br />
|
||||
<br /></div>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<div id="footer" class="noprint">
|
||||
<a href="copyright">Project Euler Copyright Information</a>
|
||||
<!--/Creative Commons License--><!-- <rdf:RDF xmlns="http://web.resource.org/cc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#">
|
||||
<Work rdf:about="">
|
||||
<license rdf:resource="http://creativecommons.org/licenses/by-nc-sa/2.0/uk/" />
|
||||
<dc:type rdf:resource="http://purl.org/dc/dcmitype/Text" />
|
||||
</Work>
|
||||
<License rdf:about="http://creativecommons.org/licenses/by-nc-sa/2.0/uk/"><permits rdf:resource="http://web.resource.org/cc/Reproduction"/><permits rdf:resource="http://web.resource.org/cc/Distribution"/><requires rdf:resource="http://web.resource.org/cc/Notice"/><requires rdf:resource="http://web.resource.org/cc/Attribution"/><prohibits rdf:resource="http://web.resource.org/cc/CommercialUse"/><permits rdf:resource="http://web.resource.org/cc/DerivativeWorks"/><requires rdf:resource="http://web.resource.org/cc/ShareAlike"/></License></rdf:RDF> -->
|
||||
</div>
|
||||
</div>
|
||||
<div style="height:1px;"> </div></body>
|
||||
</html>
|
||||
Reference in New Issue
Block a user