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\n" ); document.write( "The numbers are either 2 or 3 digits. Logical analysis and observation of patterns makes it relatively easy to find the answer.
\n" ); document.write( "(1) 2-digit numbers
\n" ); document.write( "The first digit can be any digit from 1 to 8 (8 possibilities); for each first digit there is only one digit that makes a digit sum of 8.
\n" ); document.write( "ANSWER part 1: The number of 2-digit numbers with a digit sum of 8 is 8*1 = 8.
\n" ); document.write( "(2) 3-digit numbers
\n" ); document.write( "The first digit can be any digit from 1 to 8. For each of those digits, perform the analysis similar to that used for the 2-digit numbers.
\n" ); document.write( "1st digit 1: The sum of the other 2 digits must be 7, so the second digit can be any digit from 0 to 7. That's 8 possibilities.
\n" ); document.write( "1st digit 2: The sum of the other 2 digits must be 6, so the second digit can be any digit from 0 to 6. That's 7 possibilities.
\n" ); document.write( "You can do the detailed analysis for the other first digits if you want. But it should be clear that the numbers of 3-digit numbers with other first digits will decrease by 1 for each increase of 1 in the first digit.
\n" ); document.write( "ANSWER part 2: The number of 3-digit numbers with a digit sum of 8 is 8+7+...+2+1 = 36.
\n" ); document.write( "FINAL ANSWER: The number of numbers between 10 and 1000 with a digit sum of 8 is 8+36 = 44.
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