SOLUTION: How many numbers less than 1 million do not contain the digit 2?

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Question 934615: How many numbers less than 1 million do not contain the digit 2?
Answer by KMST(5328) About Me  (Show Source):
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ANSWER:
Counting only positive integers (not counting zero),
there are 9%5E6-1=531441-1=highlight%28531440%29 numbers less than 1 million that do not contain the digit 2.
If we count zero, then it is just 531441 .

EXPLANATION:
Counting zero, numbers less than 1 million can be considered sequences of 6 digits,
0+=%22000%2C000%22 , 1=%22000%2C000%22 , ..... %22999%2C999%22 ,
so there are 10 possible choices for each digit position,
and as a consequence 10%2A10%2A10%2A10%2A10%2A10=10%5E6=%221%2C000%2C000%22 .
If we do not count 0+=%22000%2C000%22 , then there would be 1 less.
If we cannot use the digit 2 ,
there are only 9 choices for each digit position,
and we get 9%5E6=531441 6-digit sequences made from the digits 0,1,3,4,5,6,7,8,9,
including %22000%2C000%22 , which represents the number 0 .