ÿþ<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML> <HEAD> <LINK REL="stylesheet" TYPE="text/css" HREF="plays.css" /> <LINK REL="shortcut icon" HREF="favicon.ico" > <TITLE> One-Cut Checkerboard, Brain Trainer, William Armstrong </TITLE> <META NAME="Description" CONTENT="One-Cut Checkerboard at Brain Trainer Puzzles by William Armstrong"> <META NAME="Keywords" CONTENT="One-Cut Checkerboard, Brain Trainer, Puzzles, Mind, Brainteasers, visualization, medium"> </HEAD> <BODY> <!-- The following table is the logo banner and navigation bar for the page --> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="0" WIDTH="98%"> <TR> <TD VALIGN="MIDDLE" ALIGN="LEFT" WIDTH="1%" ROWSPAN="3" BGCOLOR="#111199"> <FONT FACE="Arial, Helvetica, sans-serif" SIZE="1" COLOR="#FFFFFF"> <IMG SRC="logo8.jpg" height="100" width="86" ALT="Brain logo"> </FONT> </TD> <TD BGCOLOR="#99DFFF" WIDTH="10" ROWSPAN="2"> <FONT FACE="Arial, Helvetica, sans-serif" SIZE="1" COLOR="#99DFFF">.</FONT> </TD> <TD VALIGN="BOTTOM" ALIGN="LEFT" BGCOLOR="#99DFFF"> <FONT FACE="Pythagoras, Arial, Helvetica, sans-serif" SIZE="7" COLOR="#001199"><B> Puzzles </B></FONT> </TD> <TD VALIGN="MIDDLE" ALIGN="LEFT" NOWRAP BGCOLOR="#99DFFF" COLSPAN="2"> <FONT FACE="Arial, Helvetica, sans-serif" SIZE="4" COLOR="#000000"><B> <BR>Brain Trainer<BR>by William Armstrong </B></FONT> </TD> <TD VALIGN="TOP" ALIGN="RIGHT" NOWRAP BGCOLOR="#99DFFF"> <FONT FACE="Arial, Helvetica, sans-serif" SIZE="1" COLOR="#000000"> Updated:<BR> 15 Oct 2011 </FONT> </TD> </TR> <TR> <TD VALIGN="TOP" ALIGN="LEFT" NOWRAP BGCOLOR="#99DFFF" COLSPAN="2"> <FONT FACE="Arial, Helvetica, sans-serif" SIZE="3" COLOR="#001199"><B> to Keep Your Mind Young and Agile </B></FONT> </TD> <TD VALIGN="TOP" ALIGN="RIGHT" BGCOLOR="#99DFFF" COLSPAN="2"> <FONT FACE="Arial, Helvetica, sans-serif" SIZE="2" COLOR="#000000"><B> Phone: 661-272-9393 </B></FONT> </TD> </TR> <TR BGCOLOR="#FFCC77" HEIGHT="17" WIDTH="*"> <TD VALIGN="MIDDLE" ALIGN="CENTER" COLSPAN="5" NOWRAP BGCOLOR="#001199"> <FONT FACE="Arial, Helvetica, sans-serif" SIZE="2"><B> <A HREF="index.html"><FONT COLOR="#FFFFFF">Home</FONT></A> <FONT COLOR="#FFDD88"> |</FONT> <A HREF="book1.html"><FONT COLOR="#FFFFFF">Book</FONT></A> <FONT COLOR="#FFDD88"> |</FONT> <A HREF="puzzle.html"><FONT COLOR="#FFFFFF">Puzzles</FONT></A> <FONT COLOR="#FFDD88"> |</FONT> <A HREF="mybrain.html"><FONT COLOR="#FFFFFF">Brain</FONT></A> <FONT COLOR="#FFDD88"> |</FONT> <A HREF="links.html"><FONT COLOR="#FFFFFF">Links</FONT></A> <FONT COLOR="#FFDD88"> |</FONT> <A HREF="about.html"><FONT COLOR="#FFFFFF">About Us</FONT></A> </B></FONT> </TD> </TR> </TABLE> <!-- -------- Content section begins here. -------- --> <TABLE WIDTH="100%"> <TR> <TD WIDTH="150" ALIGN="CENTER" VALIGN="TOP" BGCOLOR="#EEDDDD"> <B> <BR><A HREF="index.html">Home</A><br> <FONT SIZE=1><BR></FONT><a href="book1.html">About the Book</a><br> <FONT SIZE=1><BR></FONT><a href="puzzle.html">Puzzles</a><br> <FONT SIZE=1><BR></FONT><a href="mybrain.html">Brain Functions</a><br> <FONT SIZE=1><BR></FONT><a href="links.html">BibLINKography</a><br> <FONT SIZE=1><BR></FONT><a href="about.html">About Us</a><br> <BR><IMG SRC="spacer.gif" WIDTH="150" HEIGHT="1" BORDER="0" ALT=" "> </B> </TD> <TD> <IMG SRC="spacer.gif" WIDTH="20" HEIGHT="2"> </TD> <TD WIDTH="*" ALIGN="LEFT" VALIGN="TOP" BGCOLOR="#FFFFFF" COLOR="#003366"> <BR><CENTER><FONT SIZE=5 COLOR="#003366"><B>One-Cut Checkerboard</B></FONT> </CENTER> <TABLE> <TR> <TD ALIGN="CENTER" COLSPAN = 3><HR></TD> </TR> <TR> <TD ALIGN="LEFT" VALIGN="TOP" BGCOLOR="#FFFFFF" COLOR="#003366">Genre: Mechanical</TD> <TD ALIGN="LEFT" VALIGN="TOP" BGCOLOR="#FFFFFF" COLOR="#003366">Rating: 5 - Medium</TD> <TD ALIGN="LEFT" VALIGN="TOP" BGCOLOR="#FFFFFF" COLOR="#003366">Source: William Armstrong</TD> </TR> <TR> <TD ALIGN="LEFT" VALIGN="TOP" BGCOLOR="#FFFFFF" COLOR="#003366" COLSPAN=2>Brain Functions: Visualization / Lateral Thinking</TD> <TD ALIGN="LEFT" VALIGN="TOP" BGCOLOR="#FFFFFF" COLOR="#003366"><A HREF="mechL3hint.html">Hint</A> &nbsp;&nbsp; <A HREF="mechL3soln.html">Solution</A></TD> </TR> <TR> <TD ALIGN="CENTER" COLSPAN = 3><HR></TD> </TR> <TR> <TD ALIGN="LEFT" COLSPAN = 3> <P>Suppose we have this odd-shaped piece of wood bearing a checkered pattern. We want to make it into an 8x8 checkerboard. We could cut off the top two rows of squares, cut off the eight squares sticking out to the right, and then stack the two smaller pieces to form the missing corner. (See the smaller diagram.) However, you are only allowed to make one straight-line cut and then arrange the resulting pieces into a square checkerboard. There is a further complication: The pattern only appears on the top of the board, so you can't turn any piece face down and maintain the checkerboard pattern.</P> <CENTER><IMG SRC="mechL3.gif" ALT="One-Cut Checkerboard"> <IMG SRC="mechL3a.gif" ALT="Two-Cut Checkerboard"></CENTER> <BR> </TD> </TR> <TR> <TD ALIGN="CENTER" COLSPAN = 3>Copyright © 2011 William Armstrong</TD> </TR> <TR> <TD ALIGN="CENTER" COLSPAN = 3><HR></TD> </TR> </TABLE> </TABLE> <CENTER><BR><FONT SIZE="2"> <a href="index.html">Home</a> | <a href="book1.html">Book</a> | <a href="puzzle.html">Puzzles</A> | <a href="mybrain.html">Brain</a> | <a href="links.html">Links</a> | <a href="about.html">About Us</a> </CENTER></FONT> <br><br> <P><FONT SIZE="2">All Rights Reserved. <BR>Copyright © 2011 William Armstrong <BR>39864 Golfers Drive, Palmdale, CA 93551 USA</FONT></P> <BR><BR><BR><BR> <BR><BR><BR><BR> <BR><BR><BR><BR> </BODY> </HTML>