document.write( "Question 394292: the lockers at my school are numbered one through 250 how many times does the number nine appear \n" ); document.write( "

Algebra.Com's Answer #279890 by richard1234(7193) $\"\"$ $\"About$

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The 9 occurs in the units digits for the numbers 9, 19, 29, ..., 249 and in the tens place 90, 91, ..., 99 and 190, 191, ..., 199.\r
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\n" ); document.write( "\n" ); document.write( "We can count each case separately since they are mutually disjoint and do not affect each other (we can count 99 and 199 in both sets since the 9 occurs twice in each number). The number of elements in the set {9, 19, ..., 249} is 25 and the number of elements in the sets {90, 91, ..., 99}, {190, 191, ..., 199} is 10 times 2, or 20. The total number of 9's is 25+20, or 45. \n" ); document.write( "

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