document.write( "Question 1208708: The pages in a book are numbered from 1 to 2710. How many times was the digit 7 printed? \n" ); document.write( "

Algebra.Com's Answer #847115 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "We will count the 7s among the thousands place digits,\r\n" );
document.write( "then the hundreds place digits, then the tens place digits,\r\n" );
document.write( "and finally the one-place digits.\r\n" );
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document.write( "There are no 7's among the thousands place digits.\r\n" );
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document.write( "Among the hundreds place digits,\r\n" );
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document.write( "700-799 account for 100 hundreds place 7s,\r\n" );
document.write( "1700-1799 account for 100 hundreds place 7s,\r\n" );
document.write( "2700-2710 account for 11 hundreds place 7s\r\n" );
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document.write( "That's 211 7s among the hundredths place digits.\r\n" );
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document.write( "70-79 account for 10 tens place 7s\r\n" );
document.write( "170-79 account for 10 tens place 7s\r\n" );
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document.write( "2670-2679 account for 10 tens place 7s\r\n" );
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document.write( "That's 27x10=270 7s among the tens place digits.\r\n" );
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document.write( "[Note: from 2680 through 2710 there are no 7s in tens places.]\r\n" );
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document.write( "The 7s in ones digits occur in 7,17,27,37,...2697,2707 \r\n" );
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document.write( "That's an arithmetic sequence with a1=7, an=2707, d=10\r\n" );
document.write( "We find the number of terms:\r\n" );
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document.write( "Sum total= 211+270+271=752\r\n" );
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document.write( "There are 752 7s in all the page numbers.\r\n" );
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document.write( "Edwin

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