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bonanova

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  7. Trapped

    in New Logic/Math Puzzles

    Posted

    "How many sides does a sheet of paper have?"

    There are really two valid answers, but each makes a statement about your perception.

    If you say 2 sides, you have a fairly 2 dimensional view of the world.

    If you say six sides, then you have a more three dimensional view of the world.

    Of course, after hearing the puzzle, most people will answer 6 sides to any future inquisition.

    I have to admit that my initial answer was just two sides.

    Anyway, the relevance here is whether you consider the floor and ceiling as options or just the walls.

    If you have a three dimensional view of the world but are a little twisted,

    [a] 1 - a face or

    2 - a face and an edge.

    http://upload.wikimedia.org/wikipedia/comm...¶bius_strip.jpg

  11. The missing dollar

    in New Logic/Math Puzzles

    Posted

    The friend sold sixty marbles at 40 cents apiece [5 marbles = $2] and got $24.

    But the women expected $25.

    The mystery is not where is a missing dollar; it's why did they expect $25?

    They wanted their friend to get the same amount as if they had sold the sixty marbles separately:

    [1] one would have got $10 [30 marbles/3 marbles/$1]

    [2] the other $15 [30 marbles/2 marbles/$1]

    [Total] $25 for all sixty.

    They should have told her to sell for the average of their prices.

    Equal numbers of marbles [30] at avg price would have done it.

    AVG [33.333 cents apiece, 50 cents apiece] = 41.667 cents apiece * 60 marbles = $25.

    What they averaged was the number of marbles that each women would have sold if they had had equal dollar sales.

    But if they had had equal dollar sales, more marbles would have been sold by the first woman, at a lower than average price.

    And the combined sales would have been lower: $24 to be exact.

  13. A man visits a town and....

    in New Logic/Math Puzzles

    Posted

    Assuming the answer given by A is not subjected by whether he (A) is liar or a truth teller,

    the solution is as follows

    B said A is a liar. if B is a liar then A is a truth teller -- Man B responded "He said he was a liar.

    if B is a truth teller A is Liar

    C said A is a truth teller. If C is lair A is a liar -- Man C said "He said he was a truth teller.

    If C is a truth teller A is also a truth teller -- C in fact is a truth teller. But that does not mean A is a truth teller.

    But it is impossible to know surely because if A is a liar then would say he is truth teller But C or B would not know this

    I don't understand what you're concluding about B and C. Anything?

  15. How many balls are their?

    in New Logic/Math Puzzles

    Posted

    Change the signs on the cups to their opposite.

    The changed statements give the following possible number of balls in each cup.

    Three of the statements are now true.


    [2] _ _ 3 4
    [3] 1 2 _ _
    [4] 1 _ 3 _
    [1] _ 2 3 _

    The only number that three statements agree upon is 3.

    There are 3 balls in each cup, 12 in all.

  18. Math - Prime number

    in New Logic/Math Puzzles

    Posted

    Yeah, weird. 26 should have some significance. Here's a puzzler I ran across. Is this proveable?

    N=p1+p2 where N>2.

    Where N is a rational whole number, P1 is a prime, P2 is a prime not equal to P1.

    Well no, because primes are odd. So N couldn't be odd.

    Goldbach suggested N = p1 + p2 + p3 when N is odd.

    Let p3=1, then [N-p3] = p1 + p2.

    Since N-p3 is now even, they're essentially the same conjecture.

    Neither version has been proved - although everyone believes they're true.

  19. The Donkey and Cart Paradox

    in Paradoxes

    Posted

    This is a common Physics paradox:

    The paradox:

    A donkey starts to pull a cart (he exerts a force in one direction). The cart therefore exerts the same amount of force on the donkey (a force in the opposite direction). (Newton's third law: For every action, there is an equal and opposite reaction.) So how can the donkey pull the cart if the cart exerts the same amount of force on the donkey in the opposite direction? Should he not move?

    This is not a paradox. It's a misapplication of Newton's 3rd law.

    Newtons 2nd Law says that an object of mass m, acted upon by a net force F, experiences an acceleration a,

    in the direction of F, such that F=ma. The cart accelerates because it experiences an imbalance of forces.

    Newton's 3rd law is different. It does not apply to an object.

    It does not say that the vector sum of the forces acting upon an object is zero.

    It says that at the interface between two objects, equal and opposite forces are exerted.

    The ground, the donkey and its harness all combine to exert an unopposed force to the cart, so it accelerates.

    That happens because these objects are in contact, and Newton's 3rd law is obeyed at these points of contact.

    Take a baseball hit by Alex Rodriguez's bat. Ball and bat exert equal and opposite forces on each other [N3].

    No other force acts on the ball, so the ball accelerates. [N2]

    Because the ball exerts an equal force on the bat [N3], the bat slows down [N2].

    The motion of objects does not contradict a right application of Newton's 3rd law.

  20. Math - Prime number

    in New Logic/Math Puzzles

    Posted

    But I agree ... any prime number can be written as 6n+/-1.

    My argument is ... any prime number can be written as 2n+1.

    Actually, mine is easier in that you don't need to consider two cases -- 6n+1 and 6n-1.

    I have an even easier one: any prime number can be written as n.

    Unfortunately I can't complete the proof.

    Musings ...

    The proof works for any (3p-1); I wonder why the puzzle writer chose 26.

    299999 (300000-1) might be discouraging? -1 trivial? ["prime = n" works there.]

  21. One Girl - One Boy

    in New Logic/Math Puzzles

    Posted

    there are 3 possibilities where one child is a girl: GG, GB, BG.
    I'll add the words all and equally likely to PDR's nice explanation.

    And echo Martini's caveat that the puzzle writer's attempt to fool you often depends on your answering a question you presume is being asked.

    Read it carefully.

    For example,

    They have two kids, one of them is a girl, what is the probability that the other kid is also a girl.

    All equally likely possibilities = GG, GB, BG. Favorables = GG. Answer = 1/3.

    They have two kids, the oldest is a girl, what is the probability that the other kid is also a girl.

    All equally likely possibilities = GG, GB. Favorables = GG. Answer = 1/2.

    The possibilities must be equally likely; otherwise ...

    I just bought a lottery ticket. What's the probability I will win?

    All possibilities: It's a winning ticket, it's a losing ticket. Favorables: it's a winning ticket. Answer = 1/2

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