document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197113>Question 1197113</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Baker and co- Who is Who and Who lives Where? Messrs Carpenter, Baker and Mason live in Baker, Carpenter and Mason Streets where they practice the trades of mason, baker and carpenter. None of these men follows the trade, nor lives in the street his name suggests. Imagine how the postman mixes up the mail! Several times each week, Mr Carpenter re-addresses letters to his friend the baker. Who is who and who lives where? </SPAN>\n" );
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document.write( "If the last names matched their street names, and their professions, then we'd have this:<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Person</TD><TD >Street</TD><TD >Profession</TD></tr><tr><TD >Mr Baker</TD><TD >Baker</TD><TD >Baker</TD></tr><tr><TD >Mr Carpenter</TD><TD >Carpenter</TD><TD >Carpenter</TD></tr><tr><TD >Mr Mason</TD><TD >Mason</TD><TD >Mason</TD></tr>\n" );
document.write( "</TABLE>We have \"Baker\" all on the same row. The other two professions get their own row.\r<BR>\n" );
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document.write( "But as the instructions mention, their surnames don't match with their street name nor actual profession.\r<BR>\n" );
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document.write( "\"Mr Carpenter re-addresses letters to his friend the baker\" is basically saying \"Mr Carpenter forwards mail to his friend the baker who should have received the mail\".<BR>\n" );
document.write( "It tells us that Mr Carpenter is not the baker, or else he wouldn't forward incorrectly sent mail.\r<BR>\n" );
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document.write( "Mr Carpenter has to be the Mason since his last name doesn't match his profession. There aren't any other options left.\r<BR>\n" );
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document.write( "That forces Mr Baker to be the Carpenter and Mr Mason to be the Baker.\r<BR>\n" );
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document.write( "We have this so far.<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Person</TD><TD >Street</TD><TD >Profession</TD></tr><tr><TD >Mr Baker</TD><TD ></TD><TD >Carpenter</TD></tr><tr><TD >Mr Carpenter</TD><TD ></TD><TD >Mason</TD></tr><tr><TD >Mr Mason</TD><TD ></TD><TD >Baker</TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "Unfortunately there isn't enough info to pinpoint the street for each person.\r<BR>\n" );
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document.write( "Here are the two possibilities<BR>\n" );
document.write( "Scenario A<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Person</TD><TD >Street</TD><TD >Profession</TD></tr><tr><TD >Mr Baker</TD><TD >Carpenter</TD><TD >Carpenter</TD></tr><tr><TD >Mr Carpenter</TD><TD >Mason</TD><TD >Mason</TD></tr><tr><TD >Mr Mason</TD><TD >Baker</TD><TD >Baker</TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "Scenario B<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Person</TD><TD >Street</TD><TD >Profession</TD></tr><tr><TD >Mr Baker</TD><TD >Mason</TD><TD >Carpenter</TD></tr><tr><TD >Mr Carpenter</TD><TD >Baker</TD><TD >Mason</TD></tr><tr><TD >Mr Mason</TD><TD >Carpenter</TD><TD >Baker</TD></tr>\n" );
document.write( "</TABLE>\r<BR>\n" );
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document.write( "I suppose that the most maximum confusion for the unfortunate postman is in scenario B where not even the streets and professions line up.\r<BR>\n" );
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document.write( "What's slightly interesting about scenario B is that something like \"baker\" is found along the same diagonal (start at the top left and move toward the bottom right corner). Similarly, \"mason\" is found on a parallel diagonal, and \"carpenter\" is the same idea. \r<BR>\n" );
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document.write( "Related topic:\r<BR>\n" );
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document.write( "Consider the permutations of ABC\r<BR>\n" );
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document.write( "There are 3*2*1 = 6 of them<BR>\n" );
document.write( "ABC<BR>\n" );
document.write( "ACB<BR>\n" );
document.write( "BAC<BR>\n" );
document.write( "BCA<BR>\n" );
document.write( "CAB<BR>\n" );
document.write( "CBA\r<BR>\n" );
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document.write( "Of those 6, we have 2 where A is in the first slot (ABC and ACB). Let's erase them off the list.\r<BR>\n" );
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document.write( "Let's also erase any situation where B is in the second slot. So we'll also erase CBA<BR>\n" );
document.write( "We have this list now<BR>\n" );
document.write( "BAC<BR>\n" );
document.write( "BCA<BR>\n" );
document.write( "CAB\r<BR>\n" );
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document.write( "Let's erase BAC since C is in the third slot<BR>\n" );
document.write( "We're now left with this list of two items<BR>\n" );
document.write( "BCA<BR>\n" );
document.write( "CAB\r<BR>\n" );
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document.write( "This list represents the <a  rel=nofollow HREF= \"https://mathworld.wolfram.com/Derangement.html\">derangement</a> of {A,B,C}<BR>\n" );
document.write( "A derangement is where we scramble the letters so no letter is in its original slot. <BR>\n" );
document.write( "These 2 derangements show why we had 2 options for scenario A and scenario B earlier.\r<BR>\n" );
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document.write( "It might help to think of it like<BR>\n" );
document.write( "A = mason<BR>\n" );
document.write( "B = baker<BR>\n" );
document.write( "C = carpenter<BR>\n" );
document.write( "</font> </SPAN>\n" );
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