Car washing

Discussion in 'Physics & Math' started by Pim, May 27, 2003.

  1. ryans Come to see me about a dog hey Registered Senior Member

    Messages:
    995
    Janus58

    Good to see a semi-rigoous algebraic proof.

    Of course you probably could have written a thesis on this, stating that A,B,C... are elements of some field yada yada yada, but this is proof enough for me.

    Good stuff

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  3. MacM Registered Senior Member

    Messages:
    10,104
    Interesting

    Janus58,


    Interesting thanks. One of the tricks is to add any mixed seven digit number (1639425) across as an addition column.

    1
    6
    3
    9
    4
    2
    5+
    ---
    30

    Subtract the answer from the original number.

    1639425
    .........-30
    ------------
    1639395 ; reverse it and place it below and add.
    5939361
    -------------
    7578756; added = 45 (A multiple of 9)

    Now without having looked at the numbers you told them to perform, have them circle any digit and add the remaining in the final added answer:

    .............(8)
    i.e. 757....756 = 37. You pause and think. The next higher multiple of 9 over 37 is 45:

    "You circled an 8". (Note you can't tell the difference in them circling a "0" or a "9" so you simply say "0" or "9" if that happens.


    Another one: Write down the number 1,089 on a small piece of paper and put it in some hard to reach place. An envelope, the guests shirt pocket, etc.

    Have them write a mixed three digit number (no picket fences, i.e. 111 or 222, etc.)

    i.e.: 792

    Have them reverse the number. If it is larger in value place it above the original or if smaller place it below.


    792
    297 - Carry all "0"'s i.e. 190 becomes 091, etc. and subtract
    -------
    495 Now reverse this answer and add to the number


    495
    594 +
    -------
    1,089 Have them open the hidden paper.
     
    Last edited: Jun 4, 2003
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  5. Janus58 Valued Senior Member

    Messages:
    2,397
    Re: Interesting

    As an somewhat out of practice Amateur magician myself, I'm fairly familiar with such tricks, though I didn't really go in for the Mental Magic type tricks myself.
     
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  7. MacM Registered Senior Member

    Messages:
    10,104
    Casino

    ryans,

    Another one that will get you in trouble in the casino.

    I can shuffle a deck of cards to your satisfaction. I'll fan the cards and look at the color sequence. Then hand you the deck and have you deal the cards face down into two seperate piles based on your instinct of "Is it red or black".

    When you finish I will let you turn over one stack while I turn over the other.

    Guess what they will be in perfect color in each stack!. The dealing is totally at your will. that is on impulse 1 here, 3 there, 2 here, 5 there, 1,1, 4, etc.

    It really is impressive. Maybe we'll run into each other sometime. I'd love to show you that one. (Not how it is done of course).

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  8. MacM Registered Senior Member

    Messages:
    10,104
    Types

    Janus58,

    What type of things did you do? Cards, general silks, rings, illusions (i.e - levitation)?

    I also did a limited amount of hypnosis. Not on stage but at private parties, etc. My wife and I work on stage for about 3 years while in Europe.

    OUr car broke down once and we had to ride the Blue Goose to the show wearing an extended tail tux. That was fun.

    PS: For those not familiar with the term "Blue Goose". It refers to a bus line in France's public transportation.
     
    Last edited: Jun 4, 2003
  9. Janus58 Valued Senior Member

    Messages:
    2,397
    Re: Types

    A mixed collection of close up magic including the things you've already mentioned, plus stuff that could be adapted to a small stage/audience. The largest illusion I did was when I built a Sword box. I only did a few small stage shows,(for the some of the nearby Granges). And once entertained the kids at Camp Easter Seal. That was arranged through a friend who was working there for the summer.
     
  10. MacM Registered Senior Member

    Messages:
    10,104
    Kids

    Janus58,

    Kids are great - ahhhh. I was doing my ping pong balls from a card routine for a Boy Scout Troup once, placing the balls on a rack as I produced them and had about 18 on the rack when they couldn't stand it any more.

    They come running up on the stage, knocked over the rack and I had ping pong balls going everywhere. All you can do is laugh.

    I got started as a kid because we had a neighbor back on the farm that was a pro and he gave me an "Abbot's" catalog. I used to read the catalog like a comic book. Fascinated by all the stuff you could do. Never could afford the larger illusions though.

    Do you do the "Red & Black" pile cited above? If not I can send you a PM on how to do it.
     
    Last edited: Jun 4, 2003
  11. Pim Registered Senior Member

    Messages:
    64
    What's the next number in the following sequence?

    1
    11
    21
    1211
    111221

    When does a 4 occur for the first time?

    This is not that difficult

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  12. ryans Come to see me about a dog hey Registered Senior Member

    Messages:
    995
    Working on it.

    Got a hint?

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  13. Pim Registered Senior Member

    Messages:
    64
    It's very hard to give a hint without giving the solution

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    Try not to think too far.
     
    Last edited: Jun 26, 2003
  14. Absane Rocket Surgeon Valued Senior Member

    Messages:
    8,989
    I am going to go back to this. Although the guy won, he did not give a reason for it. So, being my natural self, I had to work it out myself.

    Let us setup three equations. The first two describe how long is takes persons A and B to wash a car.

    T_A = x*c_1
    T_B = y*c_2

    Because they are washing the same car, c_1 + c_2 = 1 (one car)

    Assume they wash different parts are the car and finish at the exact same time.

    T_A = T_B
    x*c_1 = y*c_2

    c_2 = 1 - c_1

    x*c_1 = y*(1 - c_1)

    Solving for c_1, we get
    c_1 = y/(x + y)

    Because they are finishing at the same time,
    T_A = T_B = (x*y)/(x+y)

    James Sibley
     
  15. Absane Rocket Surgeon Valued Senior Member

    Messages:
    8,989
    1
    11 (one 1)
    21 (two 1)
    1211 (one 2 one 1)
    111221 (one 1 one 2 one 1)

    Each next number describes the previous set of numbers.

    The pattern continues:

    312211
    13112221
    1113213211
    31131211121221
    13211311123112112211
    11121221123112132112212221

    I hope everyone caught on to the pattern. Notice we have yet to see a 4 in there.
    Assume that after a finite number of iterations, we find a 4. The number 4 describes how part of the last sequence was assembled.
    Let us work with this exampe and work backwards.

    41 (this means in the last seqeuce, there were four 1s
    1111 (this is part of the last sequence.)
    11 (because the last seuqnce says one 1 one 1...)

    Ok, we have worked backwards. Let us work forward now.

    11
    21
    1211
    We have a contradiction. 1211 != 41

    The other example would be something like:
    14
    4n where n is some number. This case has already been proved.

    James Sibley
     
  16. Pim Registered Senior Member

    Messages:
    64
    James: Yes that is the correct answer to the sequence, a 4 will never occur

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    The car wash riddle can be solved more easily I think.

    Person A washes the car in x hours, that is 1/x car per hour. Person B washes in the same way 1/y car per hour. Together they wash 1/x + 1/y car per hour. This means it will take them
    1/(1/x+1/y) = x*y/(x+y) hours to wash the car

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  17. Absane Rocket Surgeon Valued Senior Member

    Messages:
    8,989
    lol. Yes. Much much easier. I miss the obvious.

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    Thank you,
    James Sibley
     
  18. Absane Rocket Surgeon Valued Senior Member

    Messages:
    8,989
    Pim,

    What is your reason why 4 will never occur?

    James Sibley
     
  19. Pim Registered Senior Member

    Messages:
    64
    Because a 4 would only occur if a number would be 4 times in the previous element of the sequence, which is not possible because this can always be simplified.

    Example: 11 gives 21 and not 1111.

    But you said it very good in your post

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  20. Absane Rocket Surgeon Valued Senior Member

    Messages:
    8,989
    That was the reason I was trying to get to. I have a hard time explaining things. I may have left out one or two key points in my explaination but with some thinking, I am sure anyone can fill them in.

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    James Sibley
     
  21. Absane Rocket Surgeon Valued Senior Member

    Messages:
    8,989
    How about this...

    x^2 = x + x + x + x + ... (an x number of x's)
    d/dx [x^2] = d/dx [x + x + x + x + ...]
    2x = 1 + 1 + 1 + 1 + ...
    2x = x
    2 = 1

    Hehe... obviously something is wrong with this. Can anyone find it?

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    James Sibley
     
  22. ryans Come to see me about a dog hey Registered Senior Member

    Messages:
    995
    What

    x^2 does not equal x+x+x+x+x....That's what's wrong with it

    x^2=x.x
     
  23. Absane Rocket Surgeon Valued Senior Member

    Messages:
    8,989
    Good job

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    You solved it

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    James Sibley
     

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