document.write( "Question 838133: how many 3 digit integers greater than 499 have exactly two repeated digits \n" ); document.write( "
Algebra.Com's Answer #504963 by LinnW(1048)\"\" \"About 
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There are ten numbers with at least 2 repeated
\n" ); document.write( "digits between 500 and 599,
\n" ); document.write( "500,511,522,533,544,555,566,577,588,599.
\n" ); document.write( "Similarly there are 10 numbers
\n" ); document.write( "between 600 and 699 , 700 and 799, 800 and 899 and 900 and 999
\n" ); document.write( "This gives us 50 numbers.
\n" ); document.write( "We need to subtract 5 from 50 since
\n" ); document.write( "555,666,777,888 and 999 have three repeated digits.
\n" ); document.write( "So we end up with 45 numbers meeting the criteria.
\n" ); document.write( "We also need to account for numbers like,
\n" ); document.write( "550,551,552,553,554,555,556,557,558,559
\n" ); document.write( "There are 10 numbers above but 555 must be excluded.
\n" ); document.write( "So we are left with 9 numbers of the form 55n .
\n" ); document.write( "There are also 9 numbers of the form 66n,77n,88n,99n
\n" ); document.write( "We have 45 numbers of the forms 55n,66n,77n,88n,99n
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\n" ); document.write( "So the overall count is 45 + 45 = 90 \n" ); document.write( "
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