document.write( "Question 1178620: An SF path starts at S, follows along the edges of the
\n" ); document.write( "squares, never visits any vertex more than once, and finishes
\n" ); document.write( "at F. An example of an SF path is shown. (A vertex is a
\n" ); document.write( "point where two or more of the squares’ edges meet.)\r
\n" ); document.write( "\n" ); document.write( "This is the question (I took a screenshot):
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Algebra.Com's Answer #807949 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Consider the \"center\" of the array of squares, as shown here:
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document.write( "             f -------- g -------- X\r\n" );
document.write( "             |          |          |\r\n" );
document.write( "             |          |          |\r\n" );
document.write( "             |          |          |\r\n" );
document.write( "             |          |          |\r\n" );
document.write( "  X -------- c -------- d -------- e\r\n" );
document.write( "  |          |          |\r\n" );
document.write( "  |          |          |\r\n" );
document.write( "  |          |          |\r\n" );
document.write( "  |          |          |\r\n" );
document.write( "  X -------- a -------- b\r\n" );
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document.write( "  vertex     # of paths to that vertex\r\n" );
document.write( "  ----------------------------------------\r\n" );
document.write( "    a       C(19,0) = 1\r\n" );
document.write( "    b       C(20,0) = 1\r\n" );
document.write( "    c       C(19,1) = 19\r\n" );
document.write( "    d       = b+c = 1+19 = 20\r\n" );
document.write( "    e       = d = 20\r\n" );
document.write( "    f       = c = 19\r\n" );
document.write( "    g       = d+f = 39\r\n" );
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document.write( "Any SF path passes through exactly one of vertices e and g.\r\n" );
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document.write( "# paths g to F: C(19,0) = 1\r\n" );
document.write( "# paths e to F: C(18,1) = 18\r\n" );
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document.write( "# paths S to F: 39*1 (through g) plus 20*18 (through e) = 39+360 = 399\r\n" );
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\n" ); document.write( "ANSWER: 399 SF paths
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