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23 February, 16:34

How Many times do at least 2 odd numbers show up when you count from 0 to 999? Show your work.

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  1. 23 February, 19:32
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    let's count from 0 to 999

    0, 1, 2, 3, ooh, look, there are 2 odd numbers, 4, 5, look another one, 6, 7, another!

    we can see that every time you count from 0 to 999, at least 2 odd numbers show up

    so answer is 1 time (because if 2 odd numbers or 20 odd numbers show up, it's still at least 2 odd numbers)

    I think you really want to know how many times a pair off numbers occur together

    like 33, 313 or 333, but not 31

    that is interesting

    in the first 10's 11 is only one

    in each odd 10, in the 100's reigon, there is only 1 pair of odds

    so 11, 33, 55, 66, 77, 99 or 6 pairs in the pre-100's zone

    in the 100's zone, we have 101, 110-119, 121, 131, 141, 151, 161, 171, 181, 191 or 19 numbers with pairs of odds

    in 200's, it's the same as pre-100's, 6 pairs

    in the 300's zone, it's like 100's so 19 pairs

    in the 400 zone, it's like 200's, 6 pairs

    in 500's zone, it's like 100's, so 19 pairs

    in the 600 zone, it's like 200's, 6 pairs

    in 700's zone, it's like 100's, so 19 pairs

    in the 800 zone, it's like 200's, 6 pairs

    in 900's zone, it's like 100's, so 19 pairs

    so a total of 6+19+6+19+6+19+6+19+6+19=125 pairs of odds
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