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	<title>Comments on: Euler Problem 124</title>
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	<link>http://www.dailydoseofexcel.com/archives/2009/07/28/euler-problem-124/</link>
	<description>Daily posts of Excel tips…and other stuff</description>
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		<title>By: JoshG</title>
		<link>http://www.dailydoseofexcel.com/archives/2009/07/28/euler-problem-124/#comment-40454</link>
		<dc:creator>JoshG</dc:creator>
		<pubDate>Mon, 03 Aug 2009 16:21:00 +0000</pubDate>
		<guid isPermaLink="false">http://www.dailydoseofexcel.com/?p=2725#comment-40454</guid>
		<description>&lt;p&gt;Hi Michael,&lt;br&gt;
Thanks for posting the code.  It works fine for me - not sure what my problem was.  I managed to adapt it to solve #77.  I&#039;ll post it in your thread for #76, since it seems more appropriate there.&lt;/p&gt;
&lt;p&gt;-Josh&lt;/p&gt;
</description>
		<content:encoded><![CDATA[<p>Hi Michael,<br />
Thanks for posting the code.  It works fine for me &#8211; not sure what my problem was.  I managed to adapt it to solve #77.  I&#8217;ll post it in your thread for #76, since it seems more appropriate there.</p>
<p>-Josh</p>
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		<title>By: Michael</title>
		<link>http://www.dailydoseofexcel.com/archives/2009/07/28/euler-problem-124/#comment-40446</link>
		<dc:creator>Michael</dc:creator>
		<pubDate>Sun, 02 Aug 2009 19:35:00 +0000</pubDate>
		<guid isPermaLink="false">http://www.dailydoseofexcel.com/?p=2725#comment-40446</guid>
		<description>&lt;p&gt;Hi Tushar -&lt;/p&gt;
&lt;p&gt;Thank you, but you misunderstand...we&#039;ve both solved 31 (that code above is a different recursive solution to 31) and we&#039;re are looking therein for hint to a solution to 77.  Rather than units of currency, #77 uses prime numbers.&lt;/p&gt;
&lt;p&gt;Trying to make a fit ;-)&lt;/p&gt;
&lt;p&gt;...mrt&lt;/p&gt;
</description>
		<content:encoded><![CDATA[<p>Hi Tushar -</p>
<p>Thank you, but you misunderstand&#8230;we&#8217;ve both solved 31 (that code above is a different recursive solution to 31) and we&#8217;re are looking therein for hint to a solution to 77.  Rather than units of currency, #77 uses prime numbers.</p>
<p>Trying to make a fit <img src='http://www.dailydoseofexcel.com/wp-includes/images/smilies/icon_wink.gif' alt=';-)' class='wp-smiley' /> </p>
<p>&#8230;mrt</p>
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		<title>By: Tushar Mehta</title>
		<link>http://www.dailydoseofexcel.com/archives/2009/07/28/euler-problem-124/#comment-40445</link>
		<dc:creator>Tushar Mehta</dc:creator>
		<pubDate>Sun, 02 Aug 2009 18:51:00 +0000</pubDate>
		<guid isPermaLink="false">http://www.dailydoseofexcel.com/?p=2725#comment-40445</guid>
		<description>&lt;p&gt;Michael, Josh,&lt;/p&gt;
&lt;p&gt;If you are looking for a solution to 31 you may want to check&lt;br&gt;
Project Euler - Problem 31&lt;br&gt;
&lt;a href=&quot;http://www.tushar-mehta.com/misc_tutorials/project_euler/euler031.html&quot; rel=&quot;nofollow&quot;&gt;http://www.tushar-mehta.com/misc_tutorials/project_euler/euler031.html&lt;/a&gt;&lt;/p&gt;
</description>
		<content:encoded><![CDATA[<p>Michael, Josh,</p>
<p>If you are looking for a solution to 31 you may want to check<br />
Project Euler &#8211; Problem 31<br />
<a href="http://www.tushar-mehta.com/misc_tutorials/project_euler/euler031.html" rel="nofollow">http://www.tushar-mehta.com/misc_tutorials/project_euler/euler031.html</a></p>
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		<title>By: Michael</title>
		<link>http://www.dailydoseofexcel.com/archives/2009/07/28/euler-problem-124/#comment-40444</link>
		<dc:creator>Michael</dc:creator>
		<pubDate>Sun, 02 Aug 2009 17:56:00 +0000</pubDate>
		<guid isPermaLink="false">http://www.dailydoseofexcel.com/?p=2725#comment-40444</guid>
		<description>&lt;p&gt;Hi Josh -&lt;/p&gt;
&lt;p&gt;It runs out of stack space for me in Mac XL 2004.  Runs fine in XL2002.  For what it&#039;s worth:&lt;/p&gt;
&lt;div style=&quot;overflow: auto; white-space: nowrap;&quot; class=&quot;codecolorer-container vb default&quot;&gt;&lt;div style=&quot;white-space: nowrap;&quot; class=&quot;vb codecolorer&quot;&gt;&lt;span class=&quot;kw1&quot;&gt;Private&lt;/span&gt; coins(0 &lt;span class=&quot;kw1&quot;&gt;To&lt;/span&gt; 7) &lt;span class=&quot;kw1&quot;&gt;As&lt;/span&gt; &lt;span class=&quot;kw1&quot;&gt;Long&lt;/span&gt;&lt;br&gt;
&lt;span class=&quot;kw1&quot;&gt;Sub&lt;/span&gt; Main()&lt;br&gt;
&#160; &#160;coins(0) = 200&lt;br&gt;
&#160; &#160;coins(1) = 100&lt;br&gt;
&#160; &#160;coins(2) = 50&lt;br&gt;
&#160; &#160;coins(3) = 20&lt;br&gt;
&#160; &#160;coins(4) = 10&lt;br&gt;
&#160; &#160;coins(5) = 5&lt;br&gt;
&#160; &#160;coins(6) = 2&lt;br&gt;
&#160; &#160;coins(7) = 1&lt;br&gt;
&#160; &#160; &lt;br&gt;
&#160; &#160;Debug.&lt;span class=&quot;kw1&quot;&gt;Print&lt;/span&gt; findposs(200, 0)&lt;br&gt;
&#160; &#160;&lt;br&gt;
&lt;span class=&quot;kw1&quot;&gt;End&lt;/span&gt; &lt;span class=&quot;kw1&quot;&gt;Sub&lt;/span&gt;&lt;br&gt;
&lt;span class=&quot;kw1&quot;&gt;Function&lt;/span&gt; findposs(money &lt;span class=&quot;kw1&quot;&gt;As&lt;/span&gt; &lt;span class=&quot;kw1&quot;&gt;Long&lt;/span&gt;, maxcoin &lt;span class=&quot;kw1&quot;&gt;As&lt;/span&gt; &lt;span class=&quot;kw1&quot;&gt;Long&lt;/span&gt;) &lt;span class=&quot;kw1&quot;&gt;As&lt;/span&gt; &lt;span class=&quot;kw1&quot;&gt;Long&lt;/span&gt;&lt;br&gt;
&#160; &#160;&lt;span class=&quot;kw1&quot;&gt;Dim&lt;/span&gt; sum &lt;span class=&quot;kw1&quot;&gt;As&lt;/span&gt; &lt;span class=&quot;kw1&quot;&gt;Long&lt;/span&gt;, i &lt;span class=&quot;kw1&quot;&gt;As&lt;/span&gt; &lt;span class=&quot;kw1&quot;&gt;Long&lt;/span&gt;&lt;br&gt;
&#160; &#160;&lt;br&gt;
&#160; &#160;sum = 0&lt;br&gt;
&#160; &#160;&lt;span class=&quot;kw1&quot;&gt;If&lt;/span&gt; maxcoin = 7 &lt;span class=&quot;kw1&quot;&gt;Then&lt;/span&gt;&lt;br&gt;
&#160; &#160; &#160; findposs = 1&lt;br&gt;
&#160; &#160; &#160; &lt;span class=&quot;kw1&quot;&gt;Exit&lt;/span&gt; &lt;span class=&quot;kw1&quot;&gt;Function&lt;/span&gt;&lt;br&gt;
&#160; &#160;&lt;span class=&quot;kw1&quot;&gt;End&lt;/span&gt; &lt;span class=&quot;kw1&quot;&gt;If&lt;/span&gt;&lt;br&gt;
&#160; &#160;&lt;br&gt;
&#160; &#160;&lt;span class=&quot;kw1&quot;&gt;For&lt;/span&gt; i = maxcoin &lt;span class=&quot;kw1&quot;&gt;To&lt;/span&gt; 7&lt;br&gt;
&#160; &#160; &#160; &lt;span class=&quot;kw1&quot;&gt;If&lt;/span&gt; money - coins(i) = 0 &lt;span class=&quot;kw1&quot;&gt;Then&lt;/span&gt; sum = sum + 1&lt;br&gt;
&#160; &#160; &#160; &lt;span class=&quot;kw1&quot;&gt;If&lt;/span&gt; money - coins(i) &gt; 0 &lt;span class=&quot;kw1&quot;&gt;Then&lt;/span&gt; sum = sum + findposs(money - coins(i), i)&lt;br&gt;
&#160; &#160;&lt;span class=&quot;kw1&quot;&gt;Next&lt;/span&gt; i&lt;br&gt;
&#160; &#160;&lt;br&gt;
&#160; &#160;findposs = sum&lt;br&gt;
&#160; &#160;&lt;br&gt;
&lt;span class=&quot;kw1&quot;&gt;End&lt;/span&gt; &lt;span class=&quot;kw1&quot;&gt;Function&lt;/span&gt;&lt;/div&gt;&lt;/div&gt;
&lt;p&gt;...mrt&lt;/p&gt;
</description>
		<content:encoded><![CDATA[<p>Hi Josh -</p>
<p>It runs out of stack space for me in Mac XL 2004.  Runs fine in XL2002.  For what it&#8217;s worth:</p>
<div style="overflow: auto; white-space: nowrap;" class="codecolorer-container vb default">
<div style="white-space: nowrap;" class="vb codecolorer"><span class="kw1">Private</span> coins(0 <span class="kw1">To</span> 7) <span class="kw1">As</span> <span class="kw1">Long</span><br />
<span class="kw1">Sub</span> Main()<br />
&nbsp; &nbsp;coins(0) = 200<br />
&nbsp; &nbsp;coins(1) = 100<br />
&nbsp; &nbsp;coins(2) = 50<br />
&nbsp; &nbsp;coins(3) = 20<br />
&nbsp; &nbsp;coins(4) = 10<br />
&nbsp; &nbsp;coins(5) = 5<br />
&nbsp; &nbsp;coins(6) = 2<br />
&nbsp; &nbsp;coins(7) = 1<br />
&nbsp; &nbsp; <br />
&nbsp; &nbsp;Debug.<span class="kw1">Print</span> findposs(200, 0)<br />
&nbsp; &nbsp;<br />
<span class="kw1">End</span> <span class="kw1">Sub</span><br />
<span class="kw1">Function</span> findposs(money <span class="kw1">As</span> <span class="kw1">Long</span>, maxcoin <span class="kw1">As</span> <span class="kw1">Long</span>) <span class="kw1">As</span> <span class="kw1">Long</span><br />
&nbsp; &nbsp;<span class="kw1">Dim</span> sum <span class="kw1">As</span> <span class="kw1">Long</span>, i <span class="kw1">As</span> <span class="kw1">Long</span><br />
&nbsp; &nbsp;<br />
&nbsp; &nbsp;sum = 0<br />
&nbsp; &nbsp;<span class="kw1">If</span> maxcoin = 7 <span class="kw1">Then</span><br />
&nbsp; &nbsp; &nbsp; findposs = 1<br />
&nbsp; &nbsp; &nbsp; <span class="kw1">Exit</span> <span class="kw1">Function</span><br />
&nbsp; &nbsp;<span class="kw1">End</span> <span class="kw1">If</span><br />
&nbsp; &nbsp;<br />
&nbsp; &nbsp;<span class="kw1">For</span> i = maxcoin <span class="kw1">To</span> 7<br />
&nbsp; &nbsp; &nbsp; <span class="kw1">If</span> money &#8211; coins(i) = 0 <span class="kw1">Then</span> sum = sum + 1<br />
&nbsp; &nbsp; &nbsp; <span class="kw1">If</span> money &#8211; coins(i) &amp;gt; 0 <span class="kw1">Then</span> sum = sum + findposs(money &#8211; coins(i), i)<br />
&nbsp; &nbsp;<span class="kw1">Next</span> i<br />
&nbsp; &nbsp;<br />
&nbsp; &nbsp;findposs = sum<br />
&nbsp; &nbsp;<br />
<span class="kw1">End</span> <span class="kw1">Function</span></div>
</div>
<p>&#8230;mrt</p>
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		<title>By: JoshG</title>
		<link>http://www.dailydoseofexcel.com/archives/2009/07/28/euler-problem-124/#comment-40437</link>
		<dc:creator>JoshG</dc:creator>
		<pubDate>Sun, 02 Aug 2009 02:59:00 +0000</pubDate>
		<guid isPermaLink="false">http://www.dailydoseofexcel.com/?p=2725#comment-40437</guid>
		<description>&lt;p&gt;Michael,&lt;br&gt;
Would you mind posting your translation of #31 in VBA?  I keep running out of stack space, so I must be doing something wrong.  Thanks.&lt;/p&gt;
&lt;p&gt;-Josh&lt;/p&gt;
</description>
		<content:encoded><![CDATA[<p>Michael,<br />
Would you mind posting your translation of #31 in VBA?  I keep running out of stack space, so I must be doing something wrong.  Thanks.</p>
<p>-Josh</p>
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		<title>By: Michael</title>
		<link>http://www.dailydoseofexcel.com/archives/2009/07/28/euler-problem-124/#comment-40431</link>
		<dc:creator>Michael</dc:creator>
		<pubDate>Fri, 31 Jul 2009 21:15:00 +0000</pubDate>
		<guid isPermaLink="false">http://www.dailydoseofexcel.com/?p=2725#comment-40431</guid>
		<description>&lt;p&gt;Josh -&lt;/p&gt;
&lt;p&gt;Great thinking alike ;-)&lt;/p&gt;
&lt;p&gt;There&#039;s a neat recursive answer to #31 that drew Euler&#039;s praise right at the top.  It translates easily to VBA.  Works very well for 8 coins.  Not quite sure how to adapt it to a potful of primes.&lt;/p&gt;
&lt;p&gt;...mrt&lt;/p&gt;
</description>
		<content:encoded><![CDATA[<p>Josh -</p>
<p>Great thinking alike <img src='http://www.dailydoseofexcel.com/wp-includes/images/smilies/icon_wink.gif' alt=';-)' class='wp-smiley' /> </p>
<p>There&#8217;s a neat recursive answer to #31 that drew Euler&#8217;s praise right at the top.  It translates easily to VBA.  Works very well for 8 coins.  Not quite sure how to adapt it to a potful of primes.</p>
<p>&#8230;mrt</p>
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		<title>By: JoshG</title>
		<link>http://www.dailydoseofexcel.com/archives/2009/07/28/euler-problem-124/#comment-40430</link>
		<dc:creator>JoshG</dc:creator>
		<pubDate>Fri, 31 Jul 2009 21:03:00 +0000</pubDate>
		<guid isPermaLink="false">http://www.dailydoseofexcel.com/?p=2725#comment-40430</guid>
		<description>&lt;p&gt;Hi Michael,&lt;br&gt;
Let&#039;s just say that there are a few days where I don&#039;t get any real work done...&lt;/p&gt;
&lt;p&gt;I&#039;m having the same problems as you - I couldn&#039;t see how to re-use my #76 code for #77, and I couldn&#039;t really understand the others&#039; solutions.  There&#039;s a link to the MathWorld article on prime partitions, but I couldn&#039;t see how to apply it.  Bah.  Maybe I should go back and look at the expert solutions to #31.&lt;/p&gt;
&lt;p&gt;-Josh&lt;/p&gt;
</description>
		<content:encoded><![CDATA[<p>Hi Michael,<br />
Let&#8217;s just say that there are a few days where I don&#8217;t get any real work done&#8230;</p>
<p>I&#8217;m having the same problems as you &#8211; I couldn&#8217;t see how to re-use my #76 code for #77, and I couldn&#8217;t really understand the others&#8217; solutions.  There&#8217;s a link to the MathWorld article on prime partitions, but I couldn&#8217;t see how to apply it.  Bah.  Maybe I should go back and look at the expert solutions to #31.</p>
<p>-Josh</p>
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		<title>By: Michael</title>
		<link>http://www.dailydoseofexcel.com/archives/2009/07/28/euler-problem-124/#comment-40428</link>
		<dc:creator>Michael</dc:creator>
		<pubDate>Fri, 31 Jul 2009 20:24:00 +0000</pubDate>
		<guid isPermaLink="false">http://www.dailydoseofexcel.com/?p=2725#comment-40428</guid>
		<description>&lt;p&gt;Hi Tushar -&lt;/p&gt;
&lt;p&gt;Yep, that&#039;ll work if you can paste 100,000 rows.  But I&#039;m row-challenged still ;-)&lt;/p&gt;
&lt;p&gt;I get a nasty alert that says &quot;File not loaded completely&quot; when I  paste it. And if I can only use and sort the top 65536 rows, the correct answer is in there, but it&#039;s not even close to A10000.&lt;/p&gt;
&lt;p&gt;What I thought would be neat was a way to get 100000 rows off the web into an array.  An XL2007 webquery probably will.&lt;/p&gt;
&lt;p&gt;...mrt&lt;/p&gt;
</description>
		<content:encoded><![CDATA[<p>Hi Tushar -</p>
<p>Yep, that&#8217;ll work if you can paste 100,000 rows.  But I&#8217;m row-challenged still <img src='http://www.dailydoseofexcel.com/wp-includes/images/smilies/icon_wink.gif' alt=';-)' class='wp-smiley' /> </p>
<p>I get a nasty alert that says &#8220;File not loaded completely&#8221; when I  paste it. And if I can only use and sort the top 65536 rows, the correct answer is in there, but it&#8217;s not even close to A10000.</p>
<p>What I thought would be neat was a way to get 100000 rows off the web into an array.  An XL2007 webquery probably will.</p>
<p>&#8230;mrt</p>
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		<title>By: Tushar Mehta</title>
		<link>http://www.dailydoseofexcel.com/archives/2009/07/28/euler-problem-124/#comment-40427</link>
		<dc:creator>Tushar Mehta</dc:creator>
		<pubDate>Fri, 31 Jul 2009 19:04:00 +0000</pubDate>
		<guid isPermaLink="false">http://www.dailydoseofexcel.com/?p=2725#comment-40427</guid>
		<description>&lt;p&gt;You know what I am going to write, don&#039;t you?&lt;/p&gt;
&lt;p&gt;VBA for the cheat version?  Why?&lt;/p&gt;
&lt;p&gt;Copy the data from the web page you mentioned.&lt;/p&gt;
&lt;p&gt;Paste the data into Excel.  I put the data in cols. A and B.&lt;/p&gt;
&lt;p&gt;Sort on: B ascending then A ascending.&lt;/p&gt;
&lt;p&gt;Go to A10000.  Get the answer.&lt;/p&gt;
</description>
		<content:encoded><![CDATA[<p>You know what I am going to write, don&#8217;t you?</p>
<p>VBA for the cheat version?  Why?</p>
<p>Copy the data from the web page you mentioned.</p>
<p>Paste the data into Excel.  I put the data in cols. A and B.</p>
<p>Sort on: B ascending then A ascending.</p>
<p>Go to A10000.  Get the answer.</p>
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		<title>By: Michael</title>
		<link>http://www.dailydoseofexcel.com/archives/2009/07/28/euler-problem-124/#comment-40425</link>
		<dc:creator>Michael</dc:creator>
		<pubDate>Fri, 31 Jul 2009 18:21:00 +0000</pubDate>
		<guid isPermaLink="false">http://www.dailydoseofexcel.com/?p=2725#comment-40425</guid>
		<description>&lt;p&gt;Hi Josh -&lt;/p&gt;
&lt;p&gt;Following your steer to the BASIC statistics, Dick should reverse our roles. In one sense I&#039;m only about 30 behind you, but in the other I&#039;m about 110 behind you.  That&#039;s a lot of coding!  I better get hot ;-) &lt;/p&gt;
&lt;p&gt;There&#039;s probably few, if any, I&#039;ve done that you&#039;ve not, so I&#039;ll put #76 up anyway.  I have a good reference I can point to.  #77 is driving/drove me buggy.  I know the answer, it&#039;s in the OEIS.  I just can&#039;t &lt;i&gt;compute&lt;/i&gt; the answer.  The Haskell one-liners are no help and the one guy who put up some BASIC is so obfuscated that I can&#039;t follow his juggling indices.  I can often translate the Ruby, C, and Java, never the Python.  Those guys say they just hacked their 76 code.  Well, that&#039;s the part I can&#039;t get...&lt;/p&gt;
&lt;p&gt;Thank you for the Insertion sort...looks very useful.&lt;/p&gt;
&lt;p&gt;...mrt&lt;/p&gt;
</description>
		<content:encoded><![CDATA[<p>Hi Josh -</p>
<p>Following your steer to the BASIC statistics, Dick should reverse our roles. In one sense I&#8217;m only about 30 behind you, but in the other I&#8217;m about 110 behind you.  That&#8217;s a lot of coding!  I better get hot <img src='http://www.dailydoseofexcel.com/wp-includes/images/smilies/icon_wink.gif' alt=';-)' class='wp-smiley' />  </p>
<p>There&#8217;s probably few, if any, I&#8217;ve done that you&#8217;ve not, so I&#8217;ll put #76 up anyway.  I have a good reference I can point to.  #77 is driving/drove me buggy.  I know the answer, it&#8217;s in the OEIS.  I just can&#8217;t <i>compute</i> the answer.  The Haskell one-liners are no help and the one guy who put up some BASIC is so obfuscated that I can&#8217;t follow his juggling indices.  I can often translate the Ruby, C, and Java, never the Python.  Those guys say they just hacked their 76 code.  Well, that&#8217;s the part I can&#8217;t get&#8230;</p>
<p>Thank you for the Insertion sort&#8230;looks very useful.</p>
<p>&#8230;mrt</p>
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