document.write( "Question 352604: How many different triangles can be constructed with toothpicks by connecting the toothpicks only at their ends if each triangle can contain at most five toothpicks per side? I believe the answer is 22, I'm just not sure how I quite got that answer \n" ); document.write( "
Algebra.Com's Answer #252086 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "List them all, remembering that the sum of any two sides of a triangle\r\n" );
document.write( "must be greater than the third side.\r\n" );
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document.write( "A.  All possible triangles with 1 toothpick on one side, and no side \r\n" );
document.write( "    with more than 1 toothpick.\r\n" );
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document.write( " 1.  1,1,1\r\n" );
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document.write( "B.  All possible triangles with 2 toothpicks on one side, and no side \r\n" );
document.write( "    with more than 2 toothpicks.\r\n" );
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document.write( " 2.  2,2,2\r\n" );
document.write( " 3.  1,2,2\r\n" );
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document.write( "C.  All possible triangles with 3 toothpicks on one side, and no side \r\n" );
document.write( "    with more than 3 toothpicks.\r\n" );
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document.write( " 4.  3,3,3\r\n" );
document.write( " 5.  2,3,3\r\n" );
document.write( " 6.  1,3,3\r\n" );
document.write( " 7.  2,2,3\r\n" );
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document.write( "D.  All possible triangles with 4 toothpicks on one side, and no side \r\n" );
document.write( "    with more than 4 toothpicks.\r\n" );
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document.write( " 8.  4,4,4\r\n" );
document.write( " 9.  3,4,4\r\n" );
document.write( "10.  2,4,4\r\n" );
document.write( "11.  1,4,4\r\n" );
document.write( "12.  3,3,4\r\n" );
document.write( "13.  2,3,4\r\n" );
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document.write( "E.  All possible triangles with 5 toothpicks on one side, and\r\n" );
document.write( "    OF COURSE, no side with more than 5 toothpicks.\r\n" );
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document.write( "14.  5,5,5\r\n" );
document.write( "15.  4,5,5\r\n" );
document.write( "16.  3,5,5\r\n" );
document.write( "17.  2,5,5\r\n" );
document.write( "18.  1,5,5\r\n" );
document.write( "19.  4,4,5\r\n" );
document.write( "20.  3,4,5\r\n" );
document.write( "21.  2,4,5\r\n" );
document.write( "22.  3,4,5 \r\n" );
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document.write( "You are right!  There are 22 of them.\r\n" );
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document.write( "Edwin
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