document.write( "Question 1207225: A design is formed by arranging a certain number
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Algebra.Com's Answer #844978 by ikleyn(52855) $\"\"$ $\"About$

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A design is formed by arranging a certain number
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\n" ); document.write( "(b) 41 $\"highlight%28cross%28titles%29%29\"$ tiles
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document.write( "(a)  Consider all possible different decompositions of the number 18 into the product \r\n" );
document.write( "     of two whole numbers\r\n" );
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document.write( "         (1)  18 = 1*18\r\n" );
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document.write( "         (2)  18 = 2*9\r\n" );
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document.write( "         (3)  18 = 3*6\r\n" );
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document.write( "         (4)  18 = 6*3\r\n" );
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document.write( "         (5)  18 = 9*2\r\n" );
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document.write( "         (6)  18 = 18*1\r\n" );
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document.write( "     If you consider decompositions like (2) and (5) as different, \r\n" );
document.write( "     then the answer is \"there are 6 different designs\".\r\n" );
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document.write( "     If you consider decompositions like (2) and (5) as identical, \r\n" );
document.write( "     then the answer is \"there are 3 different designs\".\r\n" );
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document.write( "(b)  The same logic works in case (b).\r\n" );
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document.write( "     In this case, the number 41 is a prime number, so, the two possible answers are\r\n" );
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document.write( "         \"there are two possible designs, if you consider the decompositions \r\n" );
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document.write( "                  41 = 1*41\r\n" );
document.write( "              and\r\n" );
document.write( "                  41 = 41*1\r\n" );
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document.write( "          as different\"\r\n" );
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document.write( "      or \r\n" );
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document.write( "         \"there is one possible design, if you consider the decompositions \r\n" );
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document.write( "                  41 = 1*41\r\n" );
document.write( "              and\r\n" );
document.write( "                  41 = 41*1\r\n" );
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document.write( "          as identical\".\r\n" );
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