document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210196>Question 1210196</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many squares in the plane have at least two points in the lattice below as vertices?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851542 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The AI solution from the other \"tutor\" makes no sense....<br><BR>\n" );
document.write( "There is obviously only one square that has all four of those points as vertices.<br><BR>\n" );
document.write( "There are obviously no squares that have exactly 3 of those 4 points as vertices.<br><BR>\n" );
document.write( "For each pair of lattice points in the array that are adjacent vertically or horizontally, there is a square, outside of the given array, containing exactly those two given lattice points.  That's 4 more squares containing exactly 2 of the given lattice points.<br><BR>\n" );
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document.write( "For each pair of lattice points in the array that are diagonally opposite, there are 2 squares, outside of the given array, containing exactly those two given lattice points.  That's 4 more squares containing exactly 2 of the given lattice points.<br><BR>\n" );
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document.write( "So the total number of squares in the plane that have at least two of the given lattice points as vertices is 1+4+4 = 9.<br><BR>\n" );
document.write( "ANSWER: 9<br><BR>\n" );
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