SOLUTION: the lockers at my school are numbered one through 250 how many times does the number nine appear

Question 394292: the lockers at my school are numbered one through 250 how many times does the number nine appear
Found 2 solutions by layaya, richard1234:
Answer by layaya(7) (Show Source): You can put this solution on YOUR website!
25 times- 9,19,29,39,49,59,69,79,89,99,109,119,129,139,149,159,169,179,189,199,209,219,229,239,249
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
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.

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.
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