e39465ad2f
new file: Files/flashplayer_32_sa.exe
new file: favicon.ico
new file: globe.gif
new file: imgs/download.png
new file: imgs/zuck.jpg
new file: index.html
new file: other.ico
new file: script.js
new file: site.webmanifest
new file: sitemap.html
new file: styles/backround.css
new file: styles/border.css
new file: styles/fonts/Titillium_Web/OFL.txt
new file: styles/fonts/Titillium_Web/TitilliumWeb-Black.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Bold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-BoldItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLight.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Italic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Light.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-LightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Regular.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBoldItalic.ttf
new file: styles/fonts/webfontkit-20221027-163353/generator_config.txt
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-demo.html
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff2
new file: styles/fonts/webfontkit-20221027-165950/generator_config.txt
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-demo.html
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff2
new file: styles/style.css
new file: tools/2048/.gitignore
new file: tools/2048/.jshintrc
new file: tools/2048/CONTRIBUTING.md
new file: tools/2048/LICENSE.txt
new file: tools/2048/README.md
new file: tools/2048/Rakefile
new file: tools/2048/favicon.ico
new file: tools/2048/index.html
new file: tools/2048/js/animframe_polyfill.js
new file: tools/2048/js/application.js
new file: tools/2048/js/bind_polyfill.js
new file: tools/2048/js/classlist_polyfill.js
new file: tools/2048/js/game_manager.js
new file: tools/2048/js/grid.js
new file: tools/2048/js/html_actuator.js
new file: tools/2048/js/keyboard_input_manager.js
new file: tools/2048/js/local_storage_manager.js
new file: tools/2048/js/tile.js
new file: tools/2048/meta/apple-touch-icon.png
new file: tools/webretro/cores/neocd_libretro.js
new file: tools/webretro/cores/neocd_libretro.wasm
new file: tools/webretro/cores/nestopia_libretro.js
new file: tools/webretro/cores/nestopia_libretro.wasm
new file: tools/webretro/cores/o2em_libretro.js
new file: tools/webretro/cores/o2em_libretro.wasm
new file: tools/webretro/cores/opera_libretro.js
new file: tools/webretro/cores/opera_libretro.wasm
212 lines
7.3 KiB
HTML
212 lines
7.3 KiB
HTML
<!doctype html>
|
|
<html lang="en">
|
|
<!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
|
|
<!-- Mirrored from www.mathsisfun.com/pool_balls_solution.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 01:06:18 GMT -->
|
|
<head>
|
|
<meta http-equiv="content-type" content="text/html; charset=utf-8">
|
|
<!-- #BeginEditable "doctitle" -->
|
|
<title>Weighing Pool Balls Puzzle - Solution</title>
|
|
<!-- #EndEditable -->
|
|
<meta name="keywords" content="math, maths, mathematics, school, homework, education">
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
|
|
<meta name="HandheldFriendly" content="true">
|
|
<meta name="referrer" content="always">
|
|
<link rel="stylesheet" type="text/css" href="style3.css">
|
|
<script src="main3.js"></script>
|
|
</head>
|
|
|
|
<body id="bodybg">
|
|
<div class="bg">
|
|
<div id="stt"></div>
|
|
<header>
|
|
<div id="hdr"></div>
|
|
<div id="logo"><a href="index.html"><img src="images/style/logo.svg" alt="Math is Fun"></a></div>
|
|
<div id="gtran">
|
|
<script>document.write(getTrans());</script>
|
|
</div>
|
|
<div id="adTopOuter" class="centerfull noprint">
|
|
<div id="adTop">
|
|
<script>document.write(getAdTop());</script>
|
|
</div>
|
|
</div>
|
|
<div id="adHide">
|
|
<div id="showAds1"><a href="javascript:showAds()">Show Ads</a></div>
|
|
<div id="hideAds1"><a href="javascript:hideAds()">Hide Ads</a><br>
|
|
<a href="about-ads.html">About Ads</a></div>
|
|
</div>
|
|
</header>
|
|
<nav>
|
|
<div id="menuWide" class="menu">
|
|
<script>document.write(getMenu(0));</script>
|
|
</div>
|
|
<div id="linkto">
|
|
<div id="linktort">
|
|
<script>document.write(getLinks());</script>
|
|
</div>
|
|
</div>
|
|
<div id="search" role="search">
|
|
<script>document.write(getSearch());</script>
|
|
</div>
|
|
<div id="menuSlim" class="menu">
|
|
<script>document.write(getMenu(1));</script>
|
|
</div>
|
|
<div id="menuTiny" class="menu">
|
|
<script>document.write(getMenu(2));</script>
|
|
</div>
|
|
</nav>
|
|
<div id="extra"></div>
|
|
</div>
|
|
<article id="content" role="main">
|
|
<!-- #BeginEditable "Body" -->
|
|
|
|
<h1 class="center">Weighing Pool Balls - Solution</h1>
|
|
|
|
<p class="center">This is the solution to the <a href="pool_balls.html">Weighing Pool Balls Puzzle</a>.</p>
|
|
<h2>The Puzzle:</h2>
|
|
<p>You have 12 balls identical in size and appearance
|
|
but 1 is an odd weight (could be either light or heavy).</p>
|
|
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/balance-scales2.jpg" width="180" height="121" alt="balance scales" /></p>
|
|
<p>You have a set of balance scales which will give 3 possible readings:</p>
|
|
<ul>
|
|
<li>Left = Right,</li>
|
|
<li>Left > Right, or</li>
|
|
<li>Left < Right</li>
|
|
</ul>
|
|
<p>(i.e. Left and Right
|
|
have equal weight, Left is Heavier, or Left is Lighter).</p>
|
|
<p>You have <b>only 3 chances</b> to weigh the balls in any combination
|
|
using the scales.<br></p>
|
|
<p>Find which ball is the odd one and if
|
|
it's heavier or lighter than the rest.</p>
|
|
<p>How do you do it?</p>
|
|
<p> </p>
|
|
<h2>The Solution:</h2>
|
|
<p>Number the balls 1, 2, 3, ... 10, 11, 12</p>
|
|
<p>Start off with them in 3 groups: [1, 2, 3 and 4], [5, 6, 7 and
|
|
8] and [9,10,11 and 12]</p>
|
|
<p><span class="larger">Weigh <b>1, 2, 3 and 4 </b>vs <b>5, 6, 7 and
|
|
8 </b> with 3 possible outcomes:</span><br>
|
|
<br></p>
|
|
<table border="0" align="center" cellpadding="7">
|
|
<tr>
|
|
<td colspan="3" class="larger">1. If they balance then 9,10,11,12 have
|
|
the odd ball, so weigh 6,7,8 vs 9,10,11 with 3 possible outcomes:</td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td valign="top"><b>1a</b></td>
|
|
<td>If 6,7,8 vs 9,10,11 balances, 12 is the odd ball.
|
|
Weigh it against any other ball to determine if heavy or light. </td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td valign="top"><b>1b</b></td>
|
|
<td>If 9,10,11 is heavy then they contain a heavy
|
|
ball. Weigh 9 vs 10, if balanced then 11 is the odd heavy ball,
|
|
else the heavier of 9 or 10 is the odd heavy ball. </td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td valign="top"><b>1b</b></td>
|
|
<td>If 9,10,11 is light then they contain a light
|
|
ball. Weigh 9 vs 10, if balanced then 11 is the odd light ball,
|
|
else the lighter of 9 or 10 is the odd light ball. </td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td valign="top"> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td colspan="3" class="larger">2. If 5,6,7,8 > 1,2,3,4 then either 5,6,7,8
|
|
contains a heavy ball or 1,2,3,4 contains a light ball so weigh
|
|
1,2,5 vs 3,6,12 with 3 possible outcomes:</td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td valign="top"><b>2a</b></td>
|
|
<td>If 1,2,5 vs 3,6,12 balances, then either 4 is
|
|
the odd light ball or 7 or 8 is the odd heavy ball. Weigh 7
|
|
vs 8, if they balance then 4 is the odd light ball, or the heaviest
|
|
of 7 vs 8 is the odd heavy ball.</td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td valign="top"><b>2b</b></td>
|
|
<td>If 3,6,12 is heavy then either 6 is the odd heavy
|
|
ball or 1 or 2 is the odd light ball. Weigh 1 vs 2, if balanced
|
|
then 6 is the odd heavy ball, or the lightest of 1 vs 2 is the
|
|
odd light ball.</td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td valign="top"><b>2c</b></td>
|
|
<td>If 3,6,12 is light then either 3 is light or 5
|
|
is heavy. Weigh 3 against any other ball, if balanced then 5
|
|
is the odd heavy ball else 3 is the odd light ball. </td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td valign="top"> </td>
|
|
<td> </td>
|
|
</tr>
|
|
<tr>
|
|
<td colspan="3" class="larger">3. If 1,2,3,4 > 5,6,7,8 then either 1,2,3,4
|
|
contains a heavy ball or 5,6,7,8 contains a light ball so weigh
|
|
5,6,1 vs 7,2,12 with 3 possible outcomes:</td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td valign="top"><b>3a</b></td>
|
|
<td> If 5,6,1 vs 7,2,12 balances, then either 8 is
|
|
the odd light ball or 3 or 4 is the odd heavy ball. Weigh 3
|
|
vs 4, if they balance then 8 is the odd light ball, or the heaviest
|
|
of 3 vs 4 is the odd heavy ball.</td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td valign="top"><b>3b</b></td>
|
|
<td>If 7,2,12 is heavy then either 2 is the odd heavy
|
|
ball or 5 or 6 is the odd light ball. Weigh 5 vs 6, if balanced
|
|
then 2 is the odd heavy ball, or the lightest of 5 vs 6 is the
|
|
odd light ball. </td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td valign="top"><b>3c</b></td>
|
|
<td>If 7,2,12 is light then either 7 is light or 1
|
|
is heavy. Weigh 7 against any other ball, if balanced then 1
|
|
is the odd heavy ball else 7 is the odd light ball. </td>
|
|
</tr>
|
|
<tr>
|
|
<td> </td>
|
|
<td> </td>
|
|
<td> </td>
|
|
</tr>
|
|
</table>
|
|
<p><br></p>
|
|
<p><i>Puzzle supplied by Richard Rider</i></p>
|
|
|
|
<div class="related">
|
|
<a href="puzzles/index.html">Puzzles Index</a>
|
|
<a href="puzzle.html">Assorted Puzzles</a>
|
|
</div>
|
|
<!-- #EndEditable -->
|
|
|
|
</article>
|
|
<div id="adend" class="centerfull noprint">
|
|
<script>document.write(getAdEnd());</script>
|
|
</div>
|
|
<footer id="footer" class="centerfull noprint">
|
|
<script>document.write(getFooter());</script>
|
|
</footer>
|
|
<div id="copyrt">
|
|
Copyright © 2020 MathsIsFun.com
|
|
</div>
|
|
<script>document.write(getBodyEnd());</script>
|
|
</body>
|
|
<!-- #EndTemplate -->
|
|
|
|
<!-- Mirrored from www.mathsisfun.com/pool_balls_solution.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 01:06:18 GMT -->
|
|
</html>
|