Project Euler: http://projecteuler.net/
This commit is contained in:
83
ProjectEuler/pe/p430.html
Normal file
83
ProjectEuler/pe/p430.html
Normal file
@@ -0,0 +1,83 @@
|
||||
<!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 430 - 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=7b424"><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>Range flips</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 430</h3><span style="width:300px;color:#666;">Published on Sunday, 2nd June 2013, 07:00 am; Solved by 313</span></div>
|
||||
<div class="problem_content" role="problem">
|
||||
<p><var>N</var> disks are placed in a row, indexed 1 to <var>N</var> from left to right.<br>
|
||||
Each disk has a black side and white side. Initially all disks show their white side.</p>
|
||||
|
||||
<p>At each turn, two, not necessarily distinct, integers <var>A</var> and <var>B</var> between 1 and <var>N</var> (inclusive) are chosen uniformly at random.<br>
|
||||
All disks with an index from <var>A</var> to <var>B</var> (inclusive) are flipped.</p>
|
||||
|
||||
<p>The following example shows the case <var>N</var> = 8. At the first turn <var>A</var> = 5 and <var>B</var> = 2, and at the second turn <var>A</var> = 4 and <var>B</var> = 6.</p>
|
||||
|
||||
<p align=center><img src="project/images/p_430_flips.gif" /></p>
|
||||
|
||||
<p>Let E(<var>N</var>, <var>M</var>) be the expected number of disks that show their white side after <var>M</var> turns.<br>
|
||||
We can verify that E(3, 1) = 10/9, E(3, 2) = 5/3, E(10, 4) <img src='images/symbol_asymp.gif' width='11' height='9' alt='≈' border='0' style='vertical-align:middle;' /> 5.157 and E(100, 10) <img src='images/symbol_asymp.gif' width='11' height='9' alt='≈' border='0' style='vertical-align:middle;' /> 51.893.</p>
|
||||
|
||||
<p>Find E(10<sup>10</sup>, 4000).<br>
|
||||
Give your answer rounded to 2 decimal places behind the decimal point.</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