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16 November, 23:56

For how many three digit numbers (100 to 999) is the sum of the digits even? (For example, 343 has an even sum of digits: 3 + 4 + 3 = 10 which is even.) Find the answer and explain why it is correct in at least two different ways.

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  1. 17 November, 01:12
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    there are 425 numbers of three digits whose the sum of the digits is even.

    Step-by-step explanation:

    Option 1:

    It is necessary to accomplish one of the next conditions:

    (1) all of the digits are even.

    (2) exactly 2 of the digits are odd

    Then, for the first condition:

    4x5x5 = 100 - > this is because the first digit can not be 0.

    for the second condition:

    (3C1) * 5*5*5-1*5*5 = 3*125-25=350

    where 3C1 is a combination. The 3C1 determines which of the three digits is even, and it is necessary to subtract the numbers under 100 with the other 2 digits odd.

    So, there are 450 numbers of three digits whose the sum of the digits is even.

    Option 2:

    there are 900 three digit number and 5*5*5 = 125 has 3 odd numbers and 5*5*5+4*5*5+4*5*5=325 has 1 odd number, so there are 450 numbers of three digits whose the sum of the digitis is odd, so 900-450 whose the sum of the digits is even.
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