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Posers and Puzzles

Posers and Puzzles

  1. Standard member talzamir
    Art, not a Toil
    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. Subscriber sonhouse
    Fast and Curious
    24 Apr '14 11:06 / 1 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 member talzamir
    Art, not a Toil
    24 Apr '14 12:11 / 1 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. Subscriber sonhouse
    Fast and Curious
    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 member talzamir
    Art, not a Toil
    24 Apr '14 21:22 / 2 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 member smw6869
    Granny
    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.