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01_01_05.html
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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="pandoc" />
<title>Exercise 1.5</title>
<script src="site_libs/jquery-1.11.3/jquery.min.js"></script>
<meta name="viewport" content="width=device-width, initial-scale=1" />
<link href="site_libs/bootstrap-3.3.5/css/bootstrap.min.css" rel="stylesheet" />
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gtag('js', new Date());
gtag('config', 'UA-134626706-1');
</script>
<style type="text/css">code{white-space: pre;}</style>
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pre:not([class]) {
background-color: white;
}
</style>
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hljs.configure({languages: []});
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window.setTimeout(function() { hljs.initHighlighting(); }, 0);
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}
</script>
<style type="text/css">
h1 {
font-size: 34px;
}
h1.title {
font-size: 38px;
}
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}
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font-size: 24px;
}
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}
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font-size: 16px;
}
h6 {
font-size: 12px;
}
.table th:not([align]) {
text-align: left;
}
</style>
</head>
<body>
<style type = "text/css">
.main-container {
max-width: 940px;
margin-left: auto;
margin-right: auto;
}
code {
color: inherit;
background-color: rgba(0, 0, 0, 0.04);
}
img {
max-width:100%;
height: auto;
}
.tabbed-pane {
padding-top: 12px;
}
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margin-bottom: 20px;
}
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outline: none;
}
summary {
display: list-item;
}
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body {
padding-top: 51px;
padding-bottom: 40px;
}
/* offset scroll position for anchor links (for fixed navbar) */
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padding-top: 56px;
margin-top: -56px;
}
.section h2 {
padding-top: 56px;
margin-top: -56px;
}
.section h3 {
padding-top: 56px;
margin-top: -56px;
}
.section h4 {
padding-top: 56px;
margin-top: -56px;
}
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padding-top: 56px;
margin-top: -56px;
}
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padding-top: 56px;
margin-top: -56px;
}
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position: relative;
}
.dropdown-submenu>.dropdown-menu {
top: 0;
left: 100%;
margin-top: -6px;
margin-left: -1px;
border-radius: 0 6px 6px 6px;
}
.dropdown-submenu:hover>.dropdown-menu {
display: block;
}
.dropdown-submenu>a:after {
display: block;
content: " ";
float: right;
width: 0;
height: 0;
border-color: transparent;
border-style: solid;
border-width: 5px 0 5px 5px;
border-left-color: #cccccc;
margin-top: 5px;
margin-right: -10px;
}
.dropdown-submenu:hover>a:after {
border-left-color: #ffffff;
}
.dropdown-submenu.pull-left {
float: none;
}
.dropdown-submenu.pull-left>.dropdown-menu {
left: -100%;
margin-left: 10px;
border-radius: 6px 0 6px 6px;
}
</style>
<script>
// manage active state of menu based on current page
$(document).ready(function () {
// active menu anchor
href = window.location.pathname
href = href.substr(href.lastIndexOf('/') + 1)
if (href === "")
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var menuAnchor = $('a[href="' + href + '"]');
// mark it active
menuAnchor.parent().addClass('active');
// if it's got a parent navbar menu mark it active as well
menuAnchor.closest('li.dropdown').addClass('active');
});
</script>
<div class="container-fluid main-container">
<!-- tabsets -->
<style type="text/css">
.tabset-dropdown > .nav-tabs {
display: inline-table;
max-height: 500px;
min-height: 44px;
overflow-y: auto;
background: white;
border: 1px solid #ddd;
border-radius: 4px;
}
.tabset-dropdown > .nav-tabs > li.active:before {
content: "";
font-family: 'Glyphicons Halflings';
display: inline-block;
padding: 10px;
border-right: 1px solid #ddd;
}
.tabset-dropdown > .nav-tabs.nav-tabs-open > li.active:before {
content: "";
border: none;
}
.tabset-dropdown > .nav-tabs.nav-tabs-open:before {
content: "";
font-family: 'Glyphicons Halflings';
display: inline-block;
padding: 10px;
border-right: 1px solid #ddd;
}
.tabset-dropdown > .nav-tabs > li.active {
display: block;
}
.tabset-dropdown > .nav-tabs > li > a,
.tabset-dropdown > .nav-tabs > li > a:focus,
.tabset-dropdown > .nav-tabs > li > a:hover {
border: none;
display: inline-block;
border-radius: 4px;
}
.tabset-dropdown > .nav-tabs.nav-tabs-open > li {
display: block;
float: none;
}
.tabset-dropdown > .nav-tabs > li {
display: none;
}
</style>
<script>
$(document).ready(function () {
window.buildTabsets("TOC");
});
$(document).ready(function () {
$('.tabset-dropdown > .nav-tabs > li').click(function () {
$(this).parent().toggleClass('nav-tabs-open')
});
});
</script>
<!-- code folding -->
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<a class="navbar-brand" href="index.html">Applied Combinatorics</a>
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<ul class="nav navbar-nav navbar-right">
</ul>
</div><!--/.nav-collapse -->
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</div><!--/.navbar -->
<div class="fluid-row" id="header">
<h1 class="title toc-ignore">Exercise 1.5</h1>
</div>
<blockquote>
<p>Show by enumeration that there are 14 bit strings of length at most 3.</p>
</blockquote>
<ol style="list-style-type: decimal">
<li><span class="math inline">\(0\)</span></li>
<li><span class="math inline">\(1\)</span></li>
<li><span class="math inline">\(00\)</span></li>
<li><span class="math inline">\(01\)</span></li>
<li><span class="math inline">\(10\)</span></li>
<li><span class="math inline">\(11\)</span></li>
<li><span class="math inline">\(000\)</span></li>
<li><span class="math inline">\(001\)</span></li>
<li><span class="math inline">\(010\)</span></li>
<li><span class="math inline">\(011\)</span></li>
<li><span class="math inline">\(100\)</span></li>
<li><span class="math inline">\(101\)</span></li>
<li><span class="math inline">\(110\)</span></li>
<li><span class="math inline">\(111\)</span></li>
</ol>
</div>
<script>
// add bootstrap table styles to pandoc tables
function bootstrapStylePandocTables() {
$('tr.header').parent('thead').parent('table').addClass('table table-condensed');
}
$(document).ready(function () {
bootstrapStylePandocTables();
});
</script>
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<script>
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