Posers and Puzzles

Posers and Puzzles

  1. Standard membertalzamir
    Art, not a Toil
    60.13N / 25.01E
    Joined
    19 Sep '11
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    46203
    24 Apr '14 07:43
    How many zero's are at the end of 1 x 2 x 3 x .... x 1,000 ?

    What's the non-zero number right before them?
  2. Standard membersonhouse
    Fast and Curious
    slatington, pa, usa
    Joined
    28 Dec '04
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    52874
    24 Apr '14 11:061 edit
    Originally posted by talzamir
    How many zero's are at the end of 1 x 2 x 3 x .... x 1,000 ?

    What's the non-zero number right before them?
    1000 factorial. I can't even get an answer in my HP calculator, it only goes up to 500!.

    I assume therefore there is a shortcut, but no idea what that would be.

    My casio poops out at 69!, which is 1.7 E98, so only up to 2 digit exponent and my HP I think only has 3 digit exponents.

    So the answer must be 248 zero's.

    I cheated🙂

    http://voices.yahoo.com/the-number-zeros-end-1000-1000-factorial-888411.html
  3. Standard membertalzamir
    Art, not a Toil
    60.13N / 25.01E
    Joined
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    24 Apr '14 12:111 edit
    Kinda funny that the answer you cheated from is wrong. ^_^

    The principle is right, of course. The zeros at the end come from the 5's and the 2's when 1000 ! is factored, and since there are more 2's than 5's, it's enough to count the fives.

    Yahoo noted correctly that every fifth number is divisible by five, so there are 200 fives. Every fifth of those is a multiple of 5^2 = 25 so those count twice; add 40 fives. Every fifth of those is a multiple of 5^3 = 125 so those count three times, add 8 more fives, for a total of 200 + 40 + 8 = 248, as yahoo claimed.

    But they missed that 5^4 = 625 which is less than 1,000, which gives one more, for a total of 249, not 248. :-P

    So.. what's the last non-zero number before the zeros start?
  4. Standard membersonhouse
    Fast and Curious
    slatington, pa, usa
    Joined
    28 Dec '04
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    52874
    24 Apr '14 16:28
    Originally posted by talzamir
    Kinda funny that the answer you cheated from is wrong. ^_^

    The principle is right, of course. The zeros at the end come from the 5's and the 2's when 1000 ! is factored, and since there are more 2's than 5's, it's enough to count the fives.

    Yahoo noted correctly that every fifth number is divisible by five, so there are 200 fives. Every fifth of those ...[text shortened]... for a total of 249, not 248. :-P

    So.. what's the last non-zero number before the zeros start?
    Can't trust anyone anymore🙂
    How many digits total are there in 1000!?
  5. Standard membertalzamir
    Art, not a Toil
    60.13N / 25.01E
    Joined
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    46203
    24 Apr '14 21:222 edits
    There are 2,568 of them as 1,000! = 10^2,567.605 = 4.02387 x 10^2,567.

    The number exists online, but was simply enough to check with excel by taking a 10-base log of 1..1000 and adding them together.
  6. Standard membersmw6869
    Granny
    Parts Unknown
    Joined
    19 Jan '07
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    73095
    29 May '14 17:27
    Originally posted by talzamir
    There are 2,568 of them as 1,000! = 10^2,567.605 = 4.02387 x 10^2,567.

    The number exists online, but was simply enough to check with excel by taking a 10-base log of 1..1000 and adding them together.
    Please stop it! PLEASE! My brain is about to explode! Where's my duct tape?



    GRANNY.
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