document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388635>Question 388635</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi,<BR>\n" );
document.write( "when you look at positive three-digit whole numbers of which the middle digit is the average of the other two digits. one example is 741. how many of these numbers exist? </SPAN>\n" );
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document.write( "when you look at positive three-digit whole numbers of which the middle digit is the average of the other two digits. one example is 741. how many of these numbers exist?\r<BR>\n" );
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document.write( "average = 1 --> sum 1st,3rd add to 2 --> 1 + 1, 2 + 0 --> 2 numbers<BR>\n" );
document.write( "ave = 2 --> sum add to 4 --> 1 + 3, 2 + 2, 3 + 1, 4 + 0 --> 4 numbers<BR>\n" );
document.write( "ave = 3 --> sum add to 6 --> 1 + 5, 2 + 4, 3 + 3, 4 + 2, 5 + 1, 6 + 0 --> 6<BR>\n" );
document.write( "ave = 4 --> sum add to 8 --> 1 + 7, 2 + 6, 3 + 5, 4 + 4, 5 + 3, 6 + 2,<BR>\n" );
document.write( "............................   7 + 1, 8 + 0 --> 8 numbers<BR>\n" );
document.write( "ave = 5 --> sum add to 10 --> 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5, 6 + 4,<BR>\n" );
document.write( "............................   7 + 3, 8 + 2, 9 + 1 --> 9<BR>\n" );
document.write( "ave = 6 --> sum add to 12 --> 3 + 9, 4 + 8, 5 + 7, 6 + 6, 7 + 5, 8 + 4,<BR>\n" );
document.write( "............................   9 + 3 --> 7<BR>\n" );
document.write( "ave = 7 --> sum add to 14 --> 5 + 9, 6 + 8, 7 + 7, 8 + 6, 9 + 5 --> 5<BR>\n" );
document.write( "ave = 8 --> sum add to 16 --> 7 + 9, 8 + 8, 9 + 7 --> 3 numbers<BR>\n" );
document.write( "ave = 9 --> sum add to 18 --> 9 + 9 --> 1 number<BR>\n" );
document.write( "2 + 4 + 6 + 8 + 9 + 7 + 5 + 3 + 1<BR>\n" );
document.write( "appears to be the sum of the digits from 1 to 9<BR>\n" );
document.write( "sum digits = n(n+1)/2 = 9(10)/2 = 90/2 = 45 numbers<BR>\n" );
document.write( "111, 210<BR>\n" );
document.write( "123, 222, 321, 420<BR>\n" );
document.write( "135, 234, 333, 432, 531, 630<BR>\n" );
document.write( "147, 246, 345, 444, 543, 642, 741, 840<BR>\n" );
document.write( "159, 258, 357, 456, 555, 654, 753, 852, 951<BR>\n" );
document.write( "369, 468, 567, 666, 765, 864, 963<BR>\n" );
document.write( "579, 678, 777, 876, 975<BR>\n" );
document.write( "789, 888, 987<BR>\n" );
document.write( "999 </SPAN>\n" );
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