https://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_1&feed=atom&action=history
1998 AHSME Problems/Problem 1 - Revision history
2024-03-29T09:08:34Z
Revision history for this page on the wiki
MediaWiki 1.31.1
https://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_1&diff=56531&oldid=prev
Nathan wailes at 18:28, 5 July 2013
2013-07-05T18:28:34Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 18:28, 5 July 2013</td>
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<tr><td colspan="2"> </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><ins style="font-weight: bold; text-decoration: none;">{{MAA Notice}}</ins></div></td></tr>
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Nathan wailes
https://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_1&diff=41264&oldid=prev
Talkinaway at 20:42, 8 August 2011
2011-08-08T20:42:13Z
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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>==Solution==</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>==Solution==</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>{<del class="diffchange diffchange-inline">{solution}</del>}</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> </div></td></tr>
<tr><td colspan="2"> </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><ins class="diffchange diffchange-inline">Looking at the list of <math>w</math> and <math>y</math> values that must match up left-to-right, we have <math>(w,y) = A(4,6), B(1,3), C(3,5), D(7,4), E(9,7)</math>.  Looking for digits that only appear once, we see that <math>9</math>, <math>6</math>, <math>1</math>, and <math>5</math> cannot match up to other digits, and thus must appear on the ends.  <math>1</math> and <math>9</math> only appear on the left, and thus their respective blocks <math>B</math> and <math>E</math> must appear on the left.  Similarly, <math>6</math> and <math>5</math> only appear on the right, and thus their blocks <math>A</math> and <math>C</math> must appear on the right-most block of their row.  Therefore, <math>D</math>, the only block without a unique digit, must be the top-center block.</ins></div></td></tr>
<tr><td colspan="2"> </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> </div></td></tr>
<tr><td colspan="2"> </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><ins class="diffchange diffchange-inline">Now that we have placed one block, <math>D</math>, we can only place block <math>E</math> to the left of <math>D</math>, and block <math>A</math> to the right of <math>D</math>.  Thus, <math>\boxed</ins>{<ins class="diffchange diffchange-inline">E</ins>}<ins class="diffchange diffchange-inline"></math> is the right answer.</ins></div></td></tr>
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<tr><td colspan="2"> </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><ins class="diffchange diffchange-inline">Completing the puzzle, the top boxes read <math>EDA</math>, while the bottom two boxes read <math>BC</math>.    </ins></div></td></tr>
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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="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>{{AHSME box|year=1998|before=First Problem|num-a=2}}</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>{{AHSME box|year=1998|before=First Problem|num-a=2}}</div></td></tr>
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Talkinaway
https://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_1&diff=41231&oldid=prev
Talkinaway: /* See Also */
2011-08-08T01:05:45Z
<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 01:05, 8 August 2011</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>{{AHSME box|year=1998|before=First Problem|num-a=<del class="diffchange diffchange-inline">10</del>}}</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>{{AHSME box|year=1998|before=First Problem|num-a=<ins class="diffchange diffchange-inline">2</ins>}}</div></td></tr>
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Talkinaway
https://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_1&diff=39328&oldid=prev
Minsoens at 19:43, 6 June 2011
2011-06-06T19:43:30Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 19:43, 6 June 2011</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><math> \mathrm{(A)\ } A \qquad \mathrm{(B) \ }B \qquad \mathrm{(C) \  } C \qquad \mathrm{(D) \  } D \qquad \mathrm{(E) \  }E  </math></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><math> \mathrm{(A)\ } A \qquad \mathrm{(B) \ }B \qquad \mathrm{(C) \  } C \qquad \mathrm{(D) \  } D \qquad \mathrm{(E) \  }E  </math></div></td></tr>
<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;"></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;"></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><del class="diffchange diffchange-inline">[[</del>1998 <del class="diffchange diffchange-inline">AHSME Problems/</del>Problem <del class="diffchange diffchange-inline">1</del>|<del class="diffchange diffchange-inline">Solution]]</del></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><ins class="diffchange diffchange-inline">==Solution==</ins></div></td></tr>
<tr><td colspan="2"> </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><ins class="diffchange diffchange-inline">{{solution}}</ins></div></td></tr>
<tr><td colspan="2"> </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> </div></td></tr>
<tr><td colspan="2"> </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><ins class="diffchange diffchange-inline">==See Also==</ins></div></td></tr>
<tr><td colspan="2"> </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><ins class="diffchange diffchange-inline">{{AHSME box|year=</ins>1998<ins class="diffchange diffchange-inline">|before=First </ins>Problem|<ins class="diffchange diffchange-inline">num-a=10}}</ins></div></td></tr>
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Minsoens
https://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_1&diff=39325&oldid=prev
BOGTRO: Created page with "== Problem 1 == Each of the sides of five congruent rectangles is labeled with an integer. In rectangle A, <math>w = 4, x = 1, y = 6, z = 9</math>. In rectangle B, <math>w = 1, x..."
2011-06-06T19:37:31Z
<p>Created page with "== Problem 1 == Each of the sides of five congruent rectangles is labeled with an integer. In rectangle A, <math>w = 4, x = 1, y = 6, z = 9</math>. In rectangle B, <math>w = 1, x..."</p>
<p><b>New page</b></p><div>== Problem 1 ==<br />
Each of the sides of five congruent rectangles is labeled with an integer. In rectangle A, <math>w = 4, x = 1, y = 6, z = 9</math>. In rectangle B, <math>w = 1, x = 0, y = 3, z = 6</math>. In rectangle C, <math>w = 3, x = 8, y = 5, z = 2</math>. In rectangle D, <math>w = 7, x = 5, y = 4, z = 8</math>. In rectangle E, <math>w = 9, x = 2, y = 7, z = 0</math>. These five rectangles are placed, without rotating or reflecting, in position as below. Which of the rectangle is the top leftmost one?<br />
<br />
<center><asy><br />
draw((0,5)--(0,7)--(3,7)--(3,5)--cycle);<br />
draw((0,4)--(9,4)--(9,2)--(6,2)--(6,0)--(0,0)--cycle);<br />
draw((3,0)--(3,4));draw((6,2)--(6,4));draw((0,2)--(6,2));<br />
label("$w$",(0,6),(-1,0));label("$x$",(1.5,7),(0,1));label("$y$",(3,6),(1,0));label("$z$",(1.5,5),(0,-1));<br />
</asy></center><br />
<br />
<math> \mathrm{(A)\ } A \qquad \mathrm{(B) \ }B \qquad \mathrm{(C) \ } C \qquad \mathrm{(D) \ } D \qquad \mathrm{(E) \ }E </math><br />
<br />
[[1998 AHSME Problems/Problem 1|Solution]]</div>
BOGTRO