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Thread: Math problems

  1. #31
    Volvogga's Avatar
    Volvogga is offline Senior Member Always Around
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    Ok, lets see... first digit pretty much has to be 2, by my count, else you risk going over.

    4 times what equals *2... 8 off the top of my head with 32, so last digit must be 8.

    A and E are most likely done then.

    so 23758... 32, carry the 3.
    20 + 3 = 23, gives us a 3, carry the 2... so far so good.
    7 time 4 plus 2 is 30, which is a 0. Doesn't work. Middle needs to equal itself in the end. Hmm... used 3, 4 no, used 5, 6 works. So 6 times 4 plus 2 is 26... good.
    4 times 3, plus 2 is 14... shit.

    ok, that didn't work.
    *thinks*
    [15 minutes later]
    ok, got it. Same steps...
    21978.
    32, 2 carry 3.
    28 and 3 is 31, 1 carry 3.
    36 and 3 is 39, 9 carry 3.
    4 and 3 is 7, 7 no carry.
    Finally 8.

    answer 87912. Good.
    A=2
    B=1
    C=9
    D=7
    E=8
    Confirm?
    Vol~

    thanks to Silverwmoon!

  2. #32
    irecinius is offline Senior Member Community Builder
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    Can't expect no less from you Volvogga!

    But you took the long way around, there is a easier way.
    I'll post just for the sake of posting:

    Its obvious that A can't be more then 2, A also has to be an even number, because its a product of a even number(4). So a has to be 2.

    Now E, E*4 has to end in 2, only number that satisfy that are 3 and 8. However with A=2 EDCBA must be at least 80,000. So 8 is the only number that satisifies both conditions

    Next B, we know that 2BCD8*4 is at least 80000 and less than 90000. B can not be more than 2 otherwise 2BCD8 * 4 would be more than 80000. we used 2 already so B must be 0 or 1. Consideing B=0. Then D8 * 4 must end in the digit 02. However there is no D that satisfies this condition. So B must be 1.

    D8*4 must end in the digits 12. The only possiblity is D=7 (78*4=312).

    Lastly for C:
    21C78 * 4 = 87C12.
    84312+400C = 87012 + 100C
    2700 = 300C
    C=2700/300 = 9
    @adonai: You said "It can't be 2 since E must then be 8 or 9, 8*4=32, 9*4=36, neither of which ends in 2."
    But 8*4 = 32 < ends in 2 XD
    "Chile is a thin and tall country"

  3. #33
    adonai is offline Senior Member Community Builder
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    Quote Originally Posted by irecinius View Post
    @adonai: You said "It can't be 2 since E must then be 8 or 9, 8*4=32, 9*4=36, neither of which ends in 2."
    But 8*4 = 32 < ends in 2 XD
    Oh, right, don't know what I was thinking there.

  4. #34
    Volvogga's Avatar
    Volvogga is offline Senior Member Always Around
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    Ah hell... that'd a been abit easier.

    Oh well, how about some Euler (hint)?

    What's φ(9) (that's phi(9))?
    Vol~

    thanks to Silverwmoon!

  5. #35
    darkus-s6 is offline Senior Member Always Around
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    hahaha, I just learn this in one of my math classes

    φ(9) = φ(3^2) = 9 * (1 - 1/3) = 6

    "sleep with me tonight, sweety" ~sakura_hana~

  6. #36
    Volvogga's Avatar
    Volvogga is offline Senior Member Always Around
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    Bingo. Could also use relative primes and GCD. ^^
    Vol~

    thanks to Silverwmoon!

  7. #37
    darkus-s6 is offline Senior Member Always Around
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    ... sorry for not posting a problem earlier, i am in exam week :S
    now here is another one:

    John sells 1000 and he has left more than half of what he originally had. If he then sells 502 he would have left less than 500. How many books did he originally had?

    "sleep with me tonight, sweety" ~sakura_hana~

  8. #38
    irecinius is offline Senior Member Community Builder
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    (x - 1000) - 502 < 500
    -1502+x < 500
    x < 2002

    e Se
    x-1000 > 1/2x
    x > 1/2x + 1000
    1/2x > 1000
    x > 2000
    Since x > 2000 and x < 2002, so: John had 2001 books...

    Proving:
    2001 - 1000 = 1001, that is indeed more then 2001/2 (that is 1000.50)
    1001 - 502 = 499, that is indeed less then 500.

    It was that easy? or I missed the point completely?
    "Chile is a thin and tall country"

  9. #39
    darkus-s6 is offline Senior Member Always Around
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    yeap, you got it right

    "sleep with me tonight, sweety" ~sakura_hana~

  10. #40
    irecinius is offline Senior Member Community Builder
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    Humm...
    Question then!

    How many are we?
    Knowing that the probability that at least two of us have birthdays on the same day is less than half, but that this would not be the case were we one more in number.


    Been 2 days... I guess people just didn't had time to sit down a bit and work on the problem.. I'll give a BIG hint.

    364/365
    = Probability
    Last edited by irecinius; 02-17-2008 at 12:51 AM. Reason: Tip: don't account leap year...
    "Chile is a thin and tall country"

 

 
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