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bonanova

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Posts posted by bonanova

  1. But, the question was what percentage of ALL numbers consists of a number 3? Not what percentage of sets. I thought it was 33% because:

    3 is in 1 to 10, 10% of the time. (3)

    3 is in 1 to 100, 19% of the time. (3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93)

    3 is in 1 to 1000, 26% of the time because every 300th number?

    Am I making sense or completely off? Doesn't there need to be a range?

    The OP gives the range as all numbers.

    As the number of digits in the number increases, the likelihood that it contains a three increases.

    In fact the fraction of N-digit numbers that contain a 3 is 1 - [.9]**N.

    Note that [.9]**N becomes 0 at infinite N.

    Fraction of 1-digit numbers with a 3 is 1-.9 = .1

    Fraction of 2-digit numbers with a 3 is 1-.81 = .19

    Fraction of 3-digit numbers with a 3 is 1-.729 = .271

    Fraction of 4-digit numbers with a 3 is 1-.6561 = .3439

    ...

    Fraction of 10-digit numbers with a 3 is 1-.3486784401 = .6513215599

    ..

    Fraction of 44-digit numbers with a 3 is 1-.00969773... = .99030227

    ..

    Fraction of infinite-digit numbers with a 3 is 1-.0000000000... = 0.9999999999.... -> 1.0

    Note there are an order of magnitude [multiple of 10] more numbers in each successive group,

    outweighing the combined numbers in all of the previous groups.

    OK, that's weird. But how about this?

    It doesn't mean that all numbers with infinite digits contain a 3! Consider the sequence 1, 11, 111, 1111, 11111, ...

    It just means that for every infinite-digited number that does not contain a 3 there are an infinite number that do.

    Finally, the same percentages hold for numbers containing a 2, 4, or 5, ... as well.

    So the fraction of all numbers that contain a 0, 1, 2, 3, 4, 5, 6, 7, 8 and a 9 is ... 1.

    Which means, if you believe in talking about percentages of infinite groups,

    that ... all numbers contain all ten digits.

    Even tho there are an infinite number of numbers that don't.

  2. The holes on the board can be colored red, green and blue

    in such a way that each move involves a hole of each color.

    Example: blue peg jumps a green peg and lands in a red hole.

    Continue making all possible moves, and every hole will eventually be colored.

    In terms of these colors, think about the starting position and

    a winning end position. Can a series of moves go from the

    starting position to a winning end position?

    In terms of colors, what happens on each move?

  3. i have tried this lots of times and would have to say that it cant be done or there is one specific way of going about it. i hate it when i sneezed cos i blew everything out of place ( i drew the board on a piece of paper and the pegs were paper too...)
    Gezundheit!

    I used a bigger board with pennies ...

    There is a proof [that it can or can't be done] and it's cute.

  4. Since we've nearly completed the task, might be interesting to compare with what others came up with.

    Picture:[url:1c45f]http://photos1.blogger.com/blogger/4320/817/1600/75%20bands%20answers.0.jpgList:1: Led Zeppelin

    2: Gun & Roses

    3: B 52s

    4: Black Flag

    5: White Zombie

    6: Smashing Pumpkins

    7: Rolling Stones

    8: White Snake

    9: The Eagles

    10: Blind Mellon

    11: Sex Pistols

    12: Queen

    13: Garbage

    14: Alice in Chains

    15: Matchbox 20

    16: The Eels

    17: Dinosaur Jr.

    18: 50 cent

    19: Beach Boys

    20: 9 Inch Nails

    21: Seal

    22: The Dead Kennedy's

    23: Madonna

    24: The Monkees

    25: Ratt

    26: Great White

    27: The Police

    28: The Oranges

    29: Radiohead

    30: Korn

    31: Lemon Heads

    32: The Blues Travelers

    33: Iron Maidon

    34: The Pixies

    35: Prince

    36: Phish

    37: Red Hot Chili Peppers

    38: Blur

    39: Twisted Sister

    40: Cowboy Junkies

    41: Gorillaz

    42: U2

    43: Crowded House

    44: Black Crows

    45: Cars

    46: BeeGees

    47: White Stripes

    48: Talking Heads

    49: Yellowman

    50: Kiss

    51: Eminem

    52: Deep Purple

    53: Pink

    54: Hole

    55: Jewel

    56: Green Day

    57: Blondie

    58: Pavement

    59: Spoon

    60: Bush

    61: Pet Shop Boys

    62: Cake

    63: Go-Gos

    64: Manic Street Performers

    65: The Postal Service

    66: Cornershop

    67: Scissor Sisters

    68: The Vines

    69: The Doors

    70: Men at Work

    71: The Cranberries

    72: The Band

    73: Cypress Hill

    74: Skinny Puppy

    75: Was

  5. Alex hadn't been seen for a week. And things just weren't

    the same at Morty's. Jamie said it was cuz he'd lost his

    last three bets to the geniuses over at Brainden. But Davey

    opined Alex was not a sore loser. He'll be back, he said.

    And it was no sooner said than Alex appeared at the door.

    All smiles. And with a strange looking board under his arm.

    Take a look, mates, he said, and laid it on the table:

    JumpPegsPuzz155.gif

    What you see here is Alex's new version of the old solitaire

    game that you play with pegs. There's one empty hole right

    there in the center, and 36 other holes each with a peg.

    You jump pegs over neighbors into empty holes, straight ahead,

    along the lines ya see there, and remove the pegs that are

    jumped. When ya can't make any more jumps, the game is over.

    And if there's only one peg left, you've won.

    Now who'll take my bet that none of ya is smart enough

    to win? The last peg doesn't have to be in the center

    hole, mind ya, but there can be only one peg standing

    at the end.

    Go ahead. Try a few games to get the idea. Then think it

    over. If ya take the bet, you've got until Friday to write

    down a winning game.

    I'd advise against it, he winked. Cuz if you try and lose, then

    I get free drinks till Christmas. Ya might be better off just

    passing it on to the Brainden crowd. ;)

    Any takers here?

    Number the holes like this.

    --------1 2 3 4

    -------5 6 7 8 9

    ---10 11 12 13 14 15

    16 17 18 [19] 20 21 22

    ---23 24 25 26 27 28

    -----29 30 31 32 33

    ------34 35 36 37

    and write moves like this:

    [1] - 6 [12] 19 - [that means: move #1 - peg 6 jumps and removes peg 12 and lands in hole 19]

    [2] - ....... etc. 35 total jumps and you win.

    Sign up now if ya want to try, then post yer solution by Friday.

    Edit:

    Take a hint from Alex's wink:

    Prove that the game can be won. Or not.

  6. huh? maybe im misunderstanding but al im doing is having the friend send one of his locks which hasnt been closed to "me" and and then I lock the box with the lock he sent me and since it was the friends lock in the first case he could open it... maybe i misread the question.

    Sorry, I misread it, both times. :blush:

    Yes that works.

    Since the OP focuses on using the box that you have, this certainly qualifies as thinking outside the box.

    Kudos to both you and WB! ;)

  7. by four letters do you mean

    [1] actually arranging the term "four letters" into 6 words or

    [2] just pick any random word and find 6 alterations to it?

    [2], actually - so long as it has four letters.

    But [1] is intriguing, also.

    How about four letters becoming

    soul fretter / tours refelt / ferret louts or fur or let set

    since there are only four vowels, it's tough to make six words ...

  8. Hmmm. This one has me stumped... for now. <!-- s:mrgreen: --><!-- s:mrgreen: -->

    A question: if we are to give the 50th, 63rd, and 100th terms, are we to assume that the terms given are 1-12 consecutively?

    Also, if there are terms stretching to the 100th term, can we safely assume that the sequence is mathmatical in nature and not based on some other finite criterion? I assume it from this

    Well, they just go on forever, they do.

    There is a one to one correspondence between the terms in the sequence and the positive integers.

    The numbers given correspond to the numbers 1-12.

    Is the 50th term 43?
    No.

    But this may be helpful:

    terms 49 and 51 are respectively 58 and 59

    terms 62 and 64 are respectively 70 and 73

    terms 99 and 101 are respectively 109 and 114

  9. Alex thought hard before going to Morty's last night after

    losing bets two nights in a row.

    But go he did, and with an extra swagger, because he had

    come up with a challenge that he felt sure no one could meet.

    You know those number series, like 1, 4, 9, 16, 25 ...

    and the like? he asked, talking to no one in particular.

    Well all the ones I've seen are like child's play. Last night

    I come up with some numbers that none of ya here can

    figure out - not in a month of Sundays.

    Then grinning he added, But if anyone should be clever

    enough, I'll buy him drinks for a month.

    Davey appeared interested and sauntered over. Alex took

    out a crumpled sheet of paper and handed it to him. On

    it were scrawled, in Alex's dirty red ink, these numbers:

    4, 5, 8, 8, 9, 9, 12, 13, 13, 13, 17, 18, ...

    Ya see them numbers, do ya? Well, they just go on forever, they

    do. And if ya figure out what they are, you'll be able to tell me the

    50th, 63rd and 100th terms. And that's what it'll take to win.

    With that, he sauntered over to shoot darts with Jamie - but not

    before hollering back, Oh, and tell writersblock he's welcome to

    give it a try, too.

  10. After being done out of a pint of O'Doule's by writersblock

    last night at Morty's, Alex conjured up a question calculated

    to get him even.

    After WB had downed his cool one, Alex proposed a double or

    nothing puzzle. To the nearest percentage point, he asked,

    what percentage of all numbers contain at least one 3?

    For example, 13, 31, 33 and 103 all contain the digit 3 at least once.

    But 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, ... well

    you get the idea ... don't contain the digit 3 even once.

    Now I know there's a lot of numbers to check, so I'll make it

    easy for ya, Alex said. I'll give you five multiple choices.

    That gives you a 20% chance even if you guess, and much

    better odds if you yer' the genius ya' make yerself out to be.

    The percent of all numbers containing at least a single "3" is:

    [1] 10%

    [2] 13%

    [3] 33%

    [4] 67%

    [5] 100%

    What was writersblock's choice, and did he win another pint?

  11. I have two questions?

    1) Do you only have one box?

    and

    2) Do/Can you have multiple locks for one key or multiple keys for one lock?

    You have only one box.

    You have one key for each of your locks, but no keys for any of your friend's locks.

    Your friend has one key for each of her locks, but no keys for any of your locks.

  12. polar bears are only in the northern hemisphere.

    the north pole is no longer covered in ice due to global warming, so it is nothing but sea water with a few icebergs floating by.

    and the only drugged out hippie that would build a house in the north pole would be santa claus; but he's a cool hippie.

    also, while the geographic north pole does not change (AFAIK), the magnetic NP changes frequently, so it's impossible to "build" a house there that's going to remain there for a long period of time;

    hence, I think the question refers to the geo NP.

    Why is there debate about this?

    The OP says four southern exposures.

    Only at the Geo NP is this the case.

  13. Another quiet night at Morty's. Until Alex came in.

    I bought a bunch of factory reject dice the other day, he said.
    They're OK except the numbers are all wrong. Mostly they have
    extra two's and three's, but this one [he held one up, far enough
    away so the numbers could not be read] has all different numbers.

    Still, the numbers aren't 1-6.

    I have a wager for anyone here who thinks he's a genius.
    I'll roll the thing three times against that wall over there.
    The bottom and back die faces won't be visible, but I'll give
    you the sum of the four faces that are visible.

    As a bonus, I'll give you the sum of the top and front faces.
    I'll buy a pint for anyone who can tell me all six numbers on the die.
    If you try and can't figure it out, you'll buy me a pint.

    He rolled the die three times and called out the numbers:

    Roll #1 = 28 and 18
    Roll #2 = 18 and 7
    Roll #3 = 22 and 6

    Jim thought for a while, then said, no way. There's too many possibilities.
    So did Ian and Jamie.
    Davey paused to scratch his beard and said, I'll try.

    Would you have taken the bet?

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