Mindbreakers .com - Puzzles and Riddles

Here is the solution.

The cannonball in the boat displaces an amount of water equal to the MASS of the cannonball. The cannonball in the water displaces an amount of water equal to the VOLUME of the cannonball. Water is unable to support the level of salinity it would take to make it as dense as a cannonball, so the first amount is definitely more than the second amount, and the water level drops.

When you are done playing in the water, you might want to go out of the water to the beach to get some tan…

The monkey is pulling down on the rope hard enough to pull itself up. This increases the tension in the rope just enough to cause the weight to rise at the same rate as the monkey, since they are of equal mass.

The wiseman tells them to switch camels.

Mirrors invert front to back, not left to right.

The popular misconception of the inversion is caused by the fact that a person when looking at another person expects him/her to face her/him, so with the left-hand side to the right. When facing oneself (in the mirror) one sees an ‘uninverted’ person.

See Martin Gardner, “Hexaflexagons and other mathematical diversions,” University of Chicago Press 1988, Chapter 16. A letter by R.D. Tschigi and J.L. Taylor published in this book states that the fundamental reason is: “Human beings are superficially and grossly bilaterally symmetrical, but subjectively and behaviorally they are relatively asymmetrical. The very fact that we can distinguish our right from our left side implies an asymettry of the perceiving system, as noted by Ernst Mach in 1900. We are thus, to a certain extent, an asymmetrical mind dwelling in a bilaterally symmetrical body, at least with respect to a casual visual inspection of our external form.”

Martin Gardner has also written the book “The Ambidextrous Universe.”

Casper has sent in the following:

‘The riddle isn’t 100% true. If one turns his head 90 degrees to the right before looking in a mirror, one will notice that up and down are being reversed! Left, right, up and down are relative expressions, therefore the meaning of these expressions depend on how they are used. In fact, the problem of the riddle is that the mirror seems to only change the image in one direction.

The reason for this phenomenon is quite easy. A mirror is a two-dimensional field and can change an image in two directions. But because a human has got only two eyes, the image is only mirrored in one direction. If a human would have three eyes (or more), the image would be mirrored completely in two directions.

Furthermore, I wonder what would be the effect for some of us who’ve got only one eye. If such a person is used looking with one eye, I expect that the image won’t change at all. Maybe someone else can give an answer to this.’

I don’t agree with him, especially on that one eye (try it out yourself, closing one eye). His way of thinking is however creative, so I thought I could not withhold his reaction.

Mr. Smith asked nine persons, who replied him different numbers. The highest number could be 8, because everybody of the 10 participants knows at least himself and his/her partner.

If the highest number of 9 different numbers is 8, this means, that the answers were: 0, 1, 2, …, 8.

Let’s call the nine persons after the answer they gave X0, X1, X2, …, X8.

Let’s look at X8. He/she shook hands with 8 persons of his/her 9 party-mates. Among these 8 persons could be X1, X2, …, only X0 could not be among them, since X0 didn’t shake hands with anybody. That is, X8 shook hands with everybody except X0 (and himself, of course). We could say, X8 didn’t know anybody at the party except X0. From this follows, that X0 must be the wife/husband of X8.

Now let’s look at X7. He/she didn’t shake hands with 2 persons. One of these two must be his/her partner. One of these two is X0, who didn’t shake hands with anybody, the other one is X1, because X1 shook hands with only one person, and this was X8. This means, that only X0 and X1 were known by X7. X0 is the partner of X8, so X1 must be the partner of X7.

Similarly: X6 didn’t shook hands with 3 persons …

Thus X6 and X2 are married couples.

Finally, X5 and X3 are partners too.

One person, X4 remains who has no partner among the nine persons interviewed by Mr. Smith. She is Mrs. Smith.

The answer to the problem: Mrs. Smith answered: 4.

You can make a graphical solution to the problem

Let’s make them take a seat around a table:

              *       *

         *                  *

        *                     *

         *                  *

              *       *

Call one of them X8, and draw straight lines to those persons, with whom he shook hands.

              X8       *

         *                  *

        *                     *

         *                  *

              *       *

Oly one asterisk has no connection to X8, this will be called X0, and they must be partners.

In the second step take another asterisk, call it X7 draw the missing 6 lines to the other asterisks, and the only asterisk that has no connection to X7, must be called X1. They must be partners too.

At the end two asterisks remain, both with 4 connections. One of them must be Mr. Smith, since he has got nine different answers. So the other asterisk stands for Mrs. Smith.

Sent in by da one and only Peter Hosszu.

Here is the solution.
- Attach a lock to the ring. Send it to her.
- She attaches her own lock and sends it back. You remove your lock and send it back to her.
- She removes her lock.

This answer did not satisfy Don Kirkham, who has a more elegant solution:

‘I am an instructor at the US Air Force Academy. The cadets here are some of the smartest young people you could ever hope to meet. My approach to teaching is not to just give them the course information, but to teach them how to use their very creative minds to solve problems. Logic puzzles are a great tool to achieve this, so I start each class with one (or more) puzzles. At the beginning of the semester, they sometimes have trouble with what most consider simple problems, but by the end of the semester, it is extremely difficult to find puzzles that they cannot solve! What is even more exciting is to watch them come up with solutions that are “better” then the book answer!

This is what happened with the “Lock on a box” puzzle. While I have seen the puzzle worded differently, which doesn’t allow their solution, I presented the puzzle just as it is printed on your site. The solution they came up with is as follows:

“Have your friend send you an open lock that only they have the key to.”

This solution reduces the cost of “sending” because only two trips are required. Also, the box only makes one trip vs. three trips in the original solution, reducing the cost even more.

While I have seen this puzzle in several places, I have never seen this solution.

Just a thought!’

Take the chicken first and come back.
Get the grain, take it accross and take the chicken back with you.
Leave the chicken and take the fox and come back.
Get the chicken…

Lets get visual:
C = chicken
G = Grain
F = fox
} = one side of river
{ = other side of river.

  C G F     }             {

    G F     }             { C

      F     }             { G

  C         }             { F G

            }		  { F G C

Because of buoyancy, the helium balloon on the string will want to move in the direction opposite the effective gravitational field existing in the car.

Thus, when the car turns the corner, the balloon will deflect towards the inside of the turn.

A so-called ‘Nobody‘ has sent in the following on this:

‘The answer you give is incorrect - the balloon will lean opposite the curve, but this has nothing to do with “gravitational fields,” which are always, for the purpose of this sort of problem, directed toward the center of the Earth. The balloon will move because it has mass, and therefore inertia, and will want to resist the pull of the curve.’

I was waiting for a reaction on this one. I completely agreed with Steven White who has sent in the following:

‘Nobody’ is correct about inertia being the key to the problem. He is incorrect about the direction the balloon will go. The key is that air is heavier than the helium, so air is what must be considered. The inertia of the air will move it towards the outside of the car. The pressure is therefore higher in the car at the outside of the curve than at the inside. The balloon, filled with the lighter gas, will move to the area of lower pressure– the inside of the curve.

Untill…

Ian Ellis had sent in the following:

�As a physics teacher, my slant on the answer is this:

Remember the movie 2001? A circular, rotating space station housed a
walkway that appeared to let a person walk with feet to the rim and head
to the centre. That person will experience a comforting contact with the
“ground” with a force similar in feel to gravity (he could drop an apple
to his feet.) How fast the apple would fall would depend on the
measurement of the radius of the walkway and the rotational speed of the
station. These could be designed to simulate the same “feel” as gravity
on earth.

However, the force producing this contact with the “ground” is a
centripetal force related to the circular motion, not the gravitational
attraction between the mass of the person and the hull. “Centripetal” is
a general term for “centre-seeking,” and the actual nature of the force
will depend on the situation. In this case, it is the reaction force of
the hull pressing on the person’s feet.

Bring in Newton’s Laws of Motion. Law (I). An object in motion will
continue to move in a straight line at constant speed unless acted upon
by a net external force. This is the Law of Inertia; inertia is the
reluctance of a body to change its state of motion. A similar statement
applies for rotational motion and a torque. (By the way, Law II covers
what happens when there IS a net force, and ties in with acceleration.
But let’s skip that.) (III) is the often cited “action-reaction” law,
best understood as “when one object pushes on a second object, then the
second object pushes back on the first with a force that is equal in
size and opposite in direction.

Now, if you tend to move in a straight line, while the hull is rotating
to a position in front of you, it is going to be constantly nudging you
towards the centre. That nudge is a force due to contact, and is the
aforementioned “centripetal” force pushing you towards the centre. Which
follows there is a reaction force where you are pushing back against the
hull. That is known as the “centrifugal” or centre-fleeing force.

What does all this mean? Well, to steer a car around a bend is to
produce the above effects, but for only a part a full circle of motion.
And a passenger with closed eyes feels “thrown” towards the outside
door. Change your perspective to a line from the centre of the curve
outwards, and the passenger is “falling” towards the door. (To repeat,
it is in fact due to the passenger’s inertia continuing in straight-line
motion while the car door moves into the curve and passes in front.)

Back to “gravity.” In daily life, “gravity” is superficially regarded as
that comforting clinging to the surface of the earth as it spins,
instead of departing in straight line motion into space (like a stone
rotated on a string over your head when the string breaks.) That
goodness for the gravitational force of attraction between two masses -
you and the earth - which is the centripetal (center-seeking) force
here. Meanwhile, the layman pays no attention to this attraction. Which
is just as well, because even scientists cannot yet explain the basis of
the phenomenon of the mass-to-mass attraction.

By now, you should see the “effective” gravity as experienced by the
person in the car as he “falls” toward the outside door is a direct
analogy. Good enough for the layman. And the puzzle’s answer did say
“effective” - read “pseudo” - gravity. Layman’s gravity is the person
describing his experience from an internal perspective.

OK. Gravity and the random movement of air molecules produces an
atmosphere on the earth that is dense in the direction of “falling.”
Meanwhile, in the car rounding a curve, the air will be densest in the
direction of “fall” in a good analogy.

A balloon, even within its own dimensions, in either case will
experience a greater density of air on the side of falling, and a lesser
density on the opposite side. You see the effect as buoyancy when the
pressure difference produces a force greater than the balloon’s weight.
Since the pressure difference for its size is small, only a very
lightweight balloon will be buoyant.

So, the answer to the puzzle is valid from either a layman’s vision of
“effective” gravity, OR from an external view of the aspect of inertia.

Incidentally, you experience the same effect if you put two birthday
candles opposite and at the rim of a rotating record turntable. The
flames will point towards the center. Here, the flame “rises” as its
gases become hotter and less dense by expansion. The ball of warm gas
behaves just like a helium balloon without its rubber envelope.

How about that!�

Well, how about that…, I don�t think anyone can beat you, Ian, giving such a detailed and argumented explanation !

Okay, Maty Yeminy had a remark on this. In the end, I also like a simple explanation for an seemingly difficult problem. That’s what the Mind Breakers is all about: Only the best puzzles and riddles ! If you want quantity, please go to the “Rec.Puzzles Archives” on the main page or other puzzle sites.

‘The previous answer you got from “nobody” had it all. The last answer
from Ian did not add anything. Just a very long explanation of nothing
more than what was already given. All the rest is completely
superfluous.

What I say here is also no addition to what was already given by
“nobody” but it surely encompasses all that Ian has given.

It is this simple.

The reason a bowling ball will move to the outside of the curve is that
it has inertia. Air has inertia too. However the bowling ball’s inertia
is greater and therefore it will tell the air that wants to move to the
outside of the curve: No way, you are going to the inside. I have more
inertia, I will displace you and send you to the inside because I want
to go outside.

Now, this is exactly what the air says to the helium baloon because it
has more inertia.

That’s it. Whoever has more inertia wins, and the other is displaced to
the inside of the curve.

The credit should go to “nobody.”‘

Tania Ake has some more creative thoughts on the motion of the balloon !

‘For the balloon question: I’m not sure if the physics professor covered
this, but your other respondents failed to take into effect that, as the car
is turning, it is also decelerating. Therefore, the balloon would not only
tilt to the outside of the car, but, more correctly, toward the driver
(assuming we are in America).’

First the two women cross the river together (10 min). Then the quick woman (5) returns (+5=15).

Now the two men cross the river (+25=40). The other woman (10) returns with the boat (+10=50).

Now both women take their last journey to be re-united with their men … (+10=60).

YES ! You made it, they have crossed the river !