document.write( "Question 1150895: We call number example, 284 is a mountain number if its middle digit is larger than any other digit. For number. How many 3-digit mountain numbers are there? \n" ); document.write( "

Algebra.Com's Answer #772460 by ikleyn(52777) $\"\"$ $\"About$

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document.write( "If the middle digit is 9, then there are 8 possibilities for the most-left digit (from 1 to 8 inclusive), \r\n" );
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document.write( "                                     and 9 possibilities for the most-right digit (from 0 to 8 inclusive).\r\n" );
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document.write( "So, there are 8*9 = 72 such mountain numbers for the middle digit 9.\r\n" );
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document.write( "For the middle digit 8, there are 7*8 = 56 mountain numbers, following the same logic.\r\n" );
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document.write( "For the middle digit 7, there are 6*7 = 42 mountain numbers.\r\n" );
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document.write( "For the middle digit 6, there are 5*6 = 30 mountain numbers.\r\n" );
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document.write( "For the middle digit 5, there are 4*5 = 20 mountain numbers.\r\n" );
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document.write( "For the middle digit 4, there are 3*4 = 12 mountain numbers.\r\n" );
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document.write( "For the middle digit 3, there are 2*3 =  6 mountain numbers.\r\n" );
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document.write( "For the middle digit 2, there are 1*2 =  2 mountain numbers.\r\n" );
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document.write( "For the middle digit 1, there are 0*1 =  0 mountain numbers.\r\n" );
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document.write( "For the middle digit 0, there are        0 mountain numbers.\r\n" );
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document.write( "The last step is to calculate the sum  72 + 56 + 42 + 30 + 20 + 12 + 6 + 2  to get the answer.\r\n" );
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