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Math Help - Problem Solving (Digits)

  1. #1
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    Problem Solving (Digits)

    How many positive integers under 1000 use only the digits 0, 1, 2 when written?
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  2. #2
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    Use all 3 digits? Like, 102 would be lowest, 201 highest?

    Or do you mean: 1,2,10,11,12,20,21,22 ...... 221,222?
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  3. #3
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    Hello, matgrl!

    How many positive integers under 1000 use only the digits 0, 1, 2 when written?

    I assume that leading zeros are not allowed.


    We could write them out and count them . . . The answer is 26.


    We can reason it out like this . . .

    There are only 2 one-digit numbers: 1 and 2.

    For two-digit numbers: there are 2 choices for the first digit
    . . and 3 choices for the second.
    There are: 2 \times 3 \,= 6 two-digit numbers.

    For three-digit numbers: there are 2 choices for the first digit,
    . . 3 choices for the second,
    . . and 3 choices for the third.
    There are: 2 \times 3 \times 3 \,= 18 three-digit numbers.

    Therefore, there are: . 2 + 6 + 18 \:=\:26 such numbers.

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  4. #4
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    three digits
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  5. #5
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    actually I think it might be 2*2*1 meaning there s only 4 choices.
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  6. #6
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    If leading 0 allowed, then 6:
    012
    021
    102
    120
    201
    210
    If not, then 4
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