What bird comes from an egg, but doesn't lay eggs?

Set 1:

#1  Why, any male bird will do... how about a rooster?

#2  9, if you pulled out 8, you could have all 7 brown socks and only 1
    white sock.  or, if you looked, you could pull out 2.

#3  Assume the volume of jars are equal:

    It will take 1 interval for jar 1 to produce 2 amoebae.  It will
    then fill up in 3hrs.  So it takes 3 hours and 3 minutes.

#4  If we define "meet" where the heads of the trains collide and the
    distance the train is from a city by the closest part of it, the
    one coming from Moscow will be closer since its tail will be closer
    to Moscow, and the one coming from St. Petersburg will be further
    away by the length of the first train.

#5  I find it difficult to believe the ladder will be covered by water
    if the boat was already floating, thus my first answer will be 10
    meters.  Although if I read the question to say:  "the tide covers
    10 centimeters [of the ladder] each hour" then the answer is
    9.7meters remain (assuming that the ladder is vertical and the
    water is relatively peaceful).

#6  Monday:     Goes to 3m then falls to 2m.
    Tuesday:    Goes to 5m then falls to 4m.
    Wednesday:  Goes to 7m then falls to 6m.
    Thursday:   Goes to top of tree.

#7  Assume mass/volume density is the same for Coke (C) and Sprite (S)

    After the first pouring, Then you'll have 100g Sprite + 1g Coke in
    one glass and 99g Coke in the other.  If coke dissolves uniformly
    in sprite and vice-versa, then when you take a spoonfull of the
    101g mixture, you'll get: 100/101g Sprite and 1/101g Coke in the
    spoon.  When you pour that into the 99g mixture, it will have
    99+1/101g Coke and 100/101g Sprite.

    So, we have 1g/101g * 100% = 0.9901% Coke in Sprite and,
        (100/101g)/100g * 100% = 0.9901% Sprite in Coke.

#8  All the tools I want?  How about a microwave?  Or is it isolated at
    this frequency too?  Am I allowed to massively pressurize the jar?
    Why not just add energy to it by moving it, stirring it... getting
    those molecules in a random motion!  Try vibrating it at a
    frequency of 2.405GHz.  Throw it against a wall a billion times
    real fast!  The possibilities are endless...

    As for cooling it, how about expanding the jar, slowing down the
    molecules by placing them under an intense, static magnetic field
    to get those molecules pointing in the same direction--using
    necessary energy to make sure that the field is truly static....a
    little harder I suppose than refrigeration.

    Oh wait, did you mean that we're to stick them in the ol'
    calorimeter and hope that they come to the equilibrium
    temperature?  Hey, they're in ideally insulated jars--what good
    would that do?

#9  Well, I don't think it seems that hard, unless there is an "answer"
    you are looking for (or shall I say "for which you are looking?")
    There are several factors to consider.

    Assumptions:

    1.  The ellipsoid/spherical interface is perfectly reflecting.
    2.  We can retrieve all of the energy stored in the vacuum by
        slowly collapsing the volume around each "coal" - taking care
        not to favor one coal over another; so we can neglect the
        energy "lost" by the fact that part of it is contained in the
        volume.
    3.  For the assumption that the coal's radiation is initially
        focused completely on the other ellipsoid is equivalent to
        stating that all radiation from each coal is radiated normal to
        the foci.

    There are three cases:

    1.  Coal is an ideal insulator:  the problem is trivial:  all the
        heat that is radiated from a differential surface area element
        of the left coal that hits the circle will reflect back to the
        same spot where it emitted.  Thus there is no net change of
        energy.  The energy from those differential elements of the
        left coal that do not hit the sphere will focus on exactly one
        other differential element of the right coal (by assumption
        #3); but since that other differential element is also
        radiating energy directly at the aforementioned element of the
        left sphere, we have a system of two differential elements
        radiating at each other.  The energy will distribute evenly
        among the two elements.  There is no net change of energy if
        they started out with the same energy.  One might complain that
        the differential elements have unequal differential areas so
        that the power radiated per unit area is different, but note
        that it is the energy difference we are interested in which is
        Power*Area--thus cancelling out the effect.

    2.  Coal is a perfect conductor:  the energy radiated per unit area
        of each coal is the same, since the surface of the coal is at
        the same temperature.  Since we assume the photons that carry
        the energy are lossless, we have essentially a perfectly
        conducting path from one coal to the other via means of the
        ellipse.

    3.  Coal is intermediate between an insulator and conductor.  The
        solution to this approaches that of 2 as time progresses.
        Since temperature is a time average phenomenon, we need not
        worry about the time required to "redistribute" about the
        surface in the unlikely event that they started off uneven.

#10 I'm getting sleepy so catch me on this if I mess up:  The one that
    is tied to the ceiling can contain more volume, because it is more
    like a sphere than the other.  the one resting on the surface will
    deform the "spherical" surface of the balloon--causing it to
    contain less volume.  All of this hinges of course on my
    (unsubstantiated) assumption that the surface area of the balloon
    will remain nearly constant.

#11 The guy had the hiccoughs? ;)

-- Gregory E. Dionne <ged@lns61.tn.cornell.edu>

Set 2:

[Subway fare]  He paid using three quarters.  Had he only wanted one
ticket, he would have only given two of them.

[Apple tree]  The standard answer is "two", under the logic that one
apple is "apple" not "apples", but that's stupid.  If you had one
apple, and someone asked "how many apples do you have?", would you
answer "I don't have apples" or "one"?

[Clock]  22 seconds; there are 2 seconds between strikes.  Does anyone
ever really get this one wrong?

[Cookies]  Of course.  Duh.  The boy can sell his cookies for 1/2c
apiece while the girl sells her for 1/3c apiece.  If the boy agrees to
the girl's proposal, he only gets 2/5c per cookie, a loss to him of
1/10c per cookie.

Simple arithmetic isn't really very puzzling, but for the record: the
first day, the boy made 150 sales for $1.50, while the girl made 100
sales for $1.00.  The second day, they make 120 combined sales for
$2.40, which they split down the middle.  The boy loses $0.30, while
the girl gains $0.20.

[Average speed]  She can't.

[Gas]  Uh, why should I?

75 cents is 3/4 of $1, which means you'll get 4/3 as much gas at 75
cents per gallon than $1 per gallon.

75 cents is 3/2 of 50 cents, which means you'll get 2/3 as much gas at
75 cents per gallon than 50 cents per gallon.

To check: at 75 cents per gallon, your $10.00 will buy 13 1/3 gallons,
which is 4/3 of 10 gallons, which is 2/3 of 20 gallons.  No problem.

[Lopsided coin]  There are several ways.  One way is this: he flips it
twice.  If it lands heads-tails, the home team kicks off.  If it lands
tails-heads, the visitors kick off.  If it shows the same face both
flips, he starts over.

[Race]  Mike can run 90 yards in the time it takes Tina to run 100
yards, therefore, he can only run 99 yards in the time it takes her to
run 110 yards.  Tina wins again.

[Mercury]  This depends on *so* many external characteristics that the
question is meaningless.

[Salary]  Both companies are in violation of the minimum wage, at least
at first.

The answer to the question is indeterminate and depends how long Sharon
remains with the companies.  After one year, Company A would have paid
$8150 and company B would have paid $8000.  After two years, Company A
would have paid $16,600 and company B would have paid $17,200.  Company
B's advantage increases thereafter.

[ Editor: on the reckoning that gives $8150 for the first year (half
  years at $8000, $8300, $8600, $8900 a year), Company A pays $4300 +
  $4450 = $8750 in the second year, $16,900 in two years. ]

-- Jonathan S. Haas <positron@blarg.net>

[ Editor: the bracketed labels in set 2 are the editor's. ]

[ Editor: another version of the salary question, posted in 1998: ]

> Which would you choose :
>
> A starting salary of $ 1000 per yr with an increase of $ 200 each
> year
> or
>
> the same starting salary with an increase of $ 50 every six months ?

-- Judy & Irv <jidic2@webtv.net>

An even more surprising formulation, and one that avoids the quibbles
that you've gotten, would be:

which would you choose:

A starting salary of $12000 per year with an increase in yearly salary
of $1000 per year or

A starting salary of $1000 per month, with an increase in monthly
salary of $7 each month?

-- Jonathan Dushoff <dushoff@gate.sinica.edu.tw>

[ Editor: no answer to either version was found in the collected
postings. ]