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2005 PMWC Problems/Problem T1 - Revision history
2024-03-29T10:52:49Z
Revision history for this page on the wiki
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1=2: /* See also */
2007-10-09T12:07:02Z
<p><span dir="auto"><span class="autocomment">See also</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 12:07, 9 October 2007</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==See also==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{PMWC box|year=2005|<del class="diffchange diffchange-inline">before</del>=<del class="diffchange diffchange-inline">First question</del>|num-a=T2}}</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{PMWC box|year=2005|<ins class="diffchange diffchange-inline">num-b</ins>=<ins class="diffchange diffchange-inline">I15</ins>|num-a=T2}}</div></td></tr>
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https://artofproblemsolving.com/wiki/index.php?title=2005_PMWC_Problems/Problem_T1&diff=17705&oldid=prev
1=2: /* See also */
2007-10-09T12:06:35Z
<p><span dir="auto"><span class="autocomment">See also</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 12:06, 9 October 2007</td>
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https://artofproblemsolving.com/wiki/index.php?title=2005_PMWC_Problems/Problem_T1&diff=17704&oldid=prev
1=2: New page: ==Problem== Call an integer "happy", if the sum of its digits is <math>10</math>. How many "happy" integers are there between <math>100</math> and <math>1000</math>? ==Solution== We hav...
2007-10-09T12:05:54Z
<p>New page: ==Problem== Call an integer "happy", if the sum of its digits is <math>10</math>. How many "happy" integers are there between <math>100</math> and <math>1000</math>? ==Solution== We hav...</p>
<p><b>New page</b></p><div>==Problem==<br />
<br />
Call an integer "happy", if the sum of its digits is <math>10</math>. How many "happy" integers are there between <math>100</math> and <math>1000</math>?<br />
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==Solution==<br />
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We have a three digit integer in the form ABC. The number of happy integers per hundred is the number of positive integer solutions to <math>B+C=10-A</math><br />
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For the one hundreds:<br />
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B+C=9: 10 solutions<br />
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two hundreds:<br />
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B+C=8: 9 solutions<br />
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so on, until there are two solutions in 9 hundreds.<br />
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<math>10+9+8\cdots+2=54</math><br />
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==See also==</div>
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