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Mathematic Black Hole

Posted 08-10-2009 at 12:57 PM by knightmare
Three guys pitch in evenly and put down $10.00 each to buy a hotel room for $30.00 total. The hotel manager realizes they should have only paid $25.00 so he decides to refund them $5.00. He gives his clerk $5.00 to give back to the guys. On his way to their room he realizes he can't evenly split $5.00 between three guys so he decides to pocket $2.00 and give each guy $1.00. So each guy has $9.00 invested in the room right? And the clerk kept $2.00 right? so basic math tells us that 9 x 3 = 27 and then 27 + 2(what the clerk kept) = 29... where is the missing dollar?

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  1. Old
    Rebel's Avatar
    Its easy. The guys all pay 10$. =30$ then they pay too much and -5$=25$ The clerk keeps 2=23$. The the clerk pay each guy 1$=20$ so 20+5+2+3=30 I win
    Posted 08-10-2009 at 09:31 PM by Rebel Rebel is offline
  2. Old
    Locutus's Avatar
    If $30 was paid, and the bill was $25, that leaves $5 in change. If the clerk shorted them by $2, that would mean they paid $28. Which means they each originally paid $9.33 when they only should have paid $8.33.

    So while they do in fact have $9 each invested in the room after they each got a $1 refund, that is because they were each overcharged by $.67. The 3 x $.67 is the two dollars that the clerk was able to keep.
    Posted 08-10-2009 at 09:46 PM by Locutus Locutus is offline
  3. Old
    blacksheep_p's Avatar
    Math logic Fail...

    I kid, I kid!
    Posted 08-10-2009 at 10:47 PM by blacksheep_p blacksheep_p is offline
    Updated 08-10-2009 at 10:48 PM by blacksheep_p (for reasons unknown)
  4. Old
    Coginator's Avatar
    Why am I taking calculus if I don't understand this?!?!
    Posted 08-10-2009 at 11:59 PM by Coginator Coginator is offline
  5. Old
    Karma's Avatar
    Calculus has the best math groupies, that's why.
    Posted 08-11-2009 at 10:54 AM by Karma Karma is offline
  6. Old
    Naga's Avatar
    I don't get it. They paid $30, then were supposed to get $5 back. The clerk kept $2. That means they received back a grand total of $28. 28/3=9.33 per person. Therefore, the way the riddle was stated is incorrect, as it contains a lie. Easy.
    Posted 08-11-2009 at 09:45 PM by Naga Naga is offline
  7. Old
    Trojan's Avatar
    Thats nothing check out this algebra
    a=b both sides multiplied by "a"
    a^2=ab add a^2 to both sides
    2a^2=a^2+ab subtract 2ab from both sides

    Now, mathematical laws tell us we can use the distributive property to factor out the 1 and 2 from both sides so we get this


    Now we can divide both sides by (a^2-ab) and we get


    How did I do it?
    Posted 08-11-2009 at 09:50 PM by Trojan Trojan is offline

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