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	<title>Discrete Ideas &#187; Lists</title>
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		<title>Significance</title>
		<link>http://www.discreteideas.com/2009/09/significance/</link>
		<comments>http://www.discreteideas.com/2009/09/significance/#comments</comments>
		<pubDate>Mon, 07 Sep 2009 02:46:26 +0000</pubDate>
		<dc:creator>The Count</dc:creator>
				<category><![CDATA[Lists]]></category>
		<category><![CDATA[Repost]]></category>
		<category><![CDATA[numbers]]></category>
		<category><![CDATA[special]]></category>

		<guid isPermaLink="false">http://www.discreteideas.com/?p=166</guid>
		<description><![CDATA[li { padding-bottom: 3px; }

<p>Someone over at Stetson University1 has compiled a list of numbers2 with the reasons they might be termed &#8220;special&#8221;.  Some of these reasons are out there, and maybe a little contrived, but I&#8217;ve found a few that I like.  Take some time to browse this list, and I&#8217;m sure you&#8217;ll [...]]]></description>
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<p><img src="/art/special/special.jpg" class="inline_pic left_pic" />Someone over at Stetson University<span class="link_id">1</span> has compiled a list of numbers<span class="link_id">2</span> with the reasons they might be termed &#8220;special&#8221;.  Some of these reasons are out there, and maybe a little contrived, but I&#8217;ve found a few that I like.  Take some time to browse this list, and I&#8217;m sure you&#8217;ll find something of interest.  If not, check out the <a href="http://www2.stetson.edu/~efriedma/numbers.html">the entire list</a>.<br clear="all" /><br />
<span id="more-166"></span><br />
0 is the additive identity.<br />
1 is the multiplicative identity.<br />
2 is the only even prime.<br />
3 is the number of spatial dimensions we live in.<br />
4 is the smallest number of colors sufficient to color all planar maps.<br />
5 is the number of Platonic solids.<br />
6 is the smallest perfect number.<br />
7 is the smallest number of faces of a regular polygon that is not constructible by straightedge and compass.<br />
8 is the largest cube in the Fibonacci sequence.<br />
12 is the smallest abundant number.<br />
13 is the number of Archimedian solids.<br />
18 is the only number (other than 0) that is twice the sum of its digits.<br />
25 is the smallest square that can be written as a sum of 2 squares.<br />
26 is the only positive number to be directly between a square and a cube.<br />
27 is the largest number that is the sum of the digits of its cube.<br />
31 is a Mersenne prime.<br />
38 is the last Roman numeral when written lexicographically.<br />
40 is the only number whose letters are in alphabetical order.<br />
42 is the 5th Catalan number.<span class="link_id">3</span><br />
46 is the number of different arrangements (up to rotation and reflection) of 9 non-attacking queens on a 9×9 chessboard.<br />
53 is the only two digit number that is reversed in hexadecimal.<br />
55 is the largest triangular number in the Fibonacci sequence.<br />
65 is the smallest number that becomes square if its reverse is either added to or subtracted from it.<br />
70 is the smallest weird number.<br />
109 has a 5th root that starts 2.555555&#8230;.<br />
110 is the smallest number that is the product of two different substrings.<br />
128 is the largest number which is not the sum of distinct squares.<br />
132 is the smallest number which is the sum of all of the 2-digit numbers that can be formed with its digits.<br />
135 = 1<super>1</super> + 3<super>2</super> + 5<super>3</super>.<br />
145 = 1! + 4! + 5! (a factorion).<br />
151 is a palindromic prime.<br />
153 = 1<super>3</super> + 5<super>3</super> + 3<super>3</super>.<br />
198 = 11 + 99 + 88.<br />
200 is the smallest number which can not be made prime by changing one of its digits.<br />
210 is the product of the first 4 primes.<br />
257 is a Fermat prime.<br />
536 is the number of solutions of the stomachion puzzle.<br />
540 is divisible by its reverse.<br />
668 is the number of legal pawn moves in Chess.<br />
762 is the starting location of 999999 in the decimal expansion of p.<br />
873 = 1! + 2! + 3! + 4! + 5! + 6!<br />
901 is the sum of the digits of the first 100 positive integers.<br />
976 has a square formed by inserting a block of digits inside itself.<br />
1229 is the number of primes less than 10000.<br />
1233 = 12<super>2</super> + 33<super>2</super>.<br />
1369 is a square whose digits are non-decreasing.<br />
1620 is a highly abundant number.<br />
1933 is a prime factor of 111111111111111111111.<br />
2239 is a prime that remains prime if any digit is deleted.<br />
2997 = 222 + 999 + 999 + 777.<br />
3094 = 21658 / 7, and each digit is contained in the equation exactly once.<br />
3313 is the smallest prime number where every digit d occurs d times.<br />
4013 is a prime factor of 1111111111111111111111111111111111.<br />
4725 is an odd abundant number.<br />
4913 is the cube of the sum of its digits.<br />
5471 contains no 0&#8242;s in base 3 through base 10.<br />
5689 is the largest 4-digit prime with strictly increasing digits.</p>
<p>What an awesome list, thanks!<br />
<br clear="all" /><br />
<span class="count_sign">The Count</span></p>
<ol>
<li><a href="http://www.stetson.edu/home/">Stetson University</a></li>
<li><a href="http://www2.stetson.edu/~efriedma/numbers.html">What&#8217;s special about this number?</a></li>
<li>Besides being &#8230; you know &#8230; the answer to Life, the Universe, and Everything.</li>
</ol>
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		<title>5 excellent reasons to play the Lottery</title>
		<link>http://www.discreteideas.com/2009/07/5-excellent-reasons-to-play-the-lottery/</link>
		<comments>http://www.discreteideas.com/2009/07/5-excellent-reasons-to-play-the-lottery/#comments</comments>
		<pubDate>Thu, 02 Jul 2009 19:33:32 +0000</pubDate>
		<dc:creator>The Count</dc:creator>
				<category><![CDATA[Lists]]></category>
		<category><![CDATA[gambling]]></category>
		<category><![CDATA[lottery]]></category>

		<guid isPermaLink="false">http://www.tankerbay.com/discrete/?p=7</guid>
		<description><![CDATA[<p>So you&#8217;re thinking of parting with a small sum of your money in return for a miniscule chance at winning the Big Prize, the Brass Ring, the Instant Retirement Bonanza, but you just can&#8217;t bring yourself to do it.  Well, here&#8217;s a few reasons you can use to rationalize that minor expense, the Lottery ticket.</p>
<p>1. [...]]]></description>
			<content:encoded><![CDATA[<p>So you&#8217;re thinking of parting with a small sum of your money in return for a miniscule chance at winning the Big Prize, the Brass Ring, the Instant Retirement Bonanza, but you just can&#8217;t bring yourself to do it.  Well, here&#8217;s a few reasons you can use to rationalize that minor expense, the Lottery ticket.</p>
<p><img src="/art/lotto/badmath.jpg" alt="Bad at Math" class="inline_pic left_pic" /><strong>1. You&#8217;re (really) bad at math.</strong> Let&#8217;s look at the numbers.  In a &#8220;standard&#8221; Lottery, say 6 balls from 1-50, the number of possible combinations is C(50,6), or roughly 16 million.  <em>That&#8217;s not so bad,</em> you think, and you&#8217;d be right, but these kinds of lotteries rarely get into the rarefied air of the $50M or $100M payout, exactly because there are so &#8220;few&#8221; combinations.  Replace that last ball with a &#8220;bonus ball&#8221; of 1-30, and now you&#8217;re at 30*C(50,5), more like 63.5M combinations (bonus balls can be the same number as any of the other balls, which greatly increases the number of possibilities).  How&#8217;re those odds looking now?  <em>Well, what if the payout is $100M!? That&#8217;s still a good bet, right?</em> It would be, if you got to keep it all.  At today&#8217;s tax rates, and taking all the money up front (which you&#8217;d be <strong>really</strong> bad at math not to do), you end up with only 30% of the payout.  I could go into how easy it is to get 2 or more winners on the same set of numbers, cutting your jackpot even more, but I think you get the point.  The Lottery is so very rarely a &#8220;good bet&#8221;.<br />
<br clear="all"/><span id="more-7"></span><br />
<img src="/art/lotto/logging.jpg" alt="Loggers" class="inline_pic right_pic" /><strong>2. You hate trees.</strong> Again, let&#8217;s look at the numbers. According to &#8220;Lottery Wars&#8221;<span class="link_id">1</span>, Lottery business in 2008 was $60 billion (with a &#8216;b&#8217;).  Let&#8217;s be generous and call it $10 per ticket sheet and 6 sheets per page of paper.  A &#8220;standard&#8221; 128 cu. ft. tree converts to about 10000 sheets of paper (an average of several sources, I&#8217;ve found counts of 9k, 11k, etc.).  So $60B in tickets turns into about <strong>100 thousand</strong> trees&#8230; in <em>one</em> year! Ok, so they probably use some portion of recycled paper, but even if that removes 90% of the trees, it&#8217;s still a large body (log) count. So if you aren&#8217;t hip to the green, Lottery&#8217;s a pretty good way to kill some off.<br />
<br clear="all"/><br />
<img src="/art/lotto/money-falling.jpg" alt="Free$" class="inline_pic left_pic" /><strong>3. You are an extreme optimist.</strong> Are you one of those people where the glass isn&#8217;t just half-full, but cut from a single diamond?  Go ahead then, play the Lottery expecting to win.  Alternatively, and with a slightly better chance of success, you could follow the next short guy in green you see to find his treasure. How about digging in your backyard for the Lost City of Gold, or even betting your friend that you&#8217;ll be struck by lightning &#8230; twice?  These all seem to have similar chances of success.<br />
<br clear="all"/><br />
<img src="/art/lotto/donate.jpg" alt="donate" class="inline_pic right_pic" /><strong>4. You really want to help [insert Lottery beneficiary here] only, not so much.</strong> Some people like to justify their Lottery purchases thinking, <em>Well, it helps the schools,</em> or some such.  Unfortunately, according to &#8220;Lottery Wars&#8221; again, on average less than 1/3 of the money collected by lotteries goes to the beneficary organization.  Furthermore, in some cases (such as the California school system), this money is not treated as a windfall, but replaces money that is redirected elsewhere in the budget.  You might be better off just buying some supplies for your local school.<br />
<br clear="all"/><br />
<img src="/art/lotto/dream.jpg" alt="dream" class="inline_pic left_pic" /><strong>5. At last, we come to the only really excellent reason to play the Lottery: to have fun!</strong> Lottery tickets make decent presents, especially for those people you don&#8217;t actually want to give anything, but feel obligated to spend money on.  They also make great conversation topics.  Run out of things to say to your spouse?  Buy some tickets and regale each other with how much fun you&#8217;ll have together if you win, or even apart after the divorce you can now afford.  Dreaming about vacations, home and car renovations, and gifts to loved ones is the biggest value from buying a Lottery ticket.  Enjoy!<br />
<br clear="all"/><br />
<span class="count_sign">The Count</span></p>
<hr width="66%"/>
<ol>
<li><a href="http://www.amazon.com/gp/product/1596913045?ie=UTF8&amp;tag=foost-20&amp;linkCode=as2&amp;camp=1789&amp;creative=9325&amp;creativeASIN=1596913045">The Lottery Wars, by Matthew Sweeney</a></li>
<li><a href="http://en.wikipedia.org/wiki/Lottery">Lottery on Wikipedia</a></li>
</ol>
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