The worlds first riddle!

OK, then. Since it is a stick shift, I'd say I could drive exactly zero miles.

Mark, who is on a roll wrote:

This dish is not wholesome.
My gardener is very old. (I suggest you get the butler to cut the grass)
Humming birds are not large birds.

WENDY
Thursday - lion told the truth, unicorn lied

An Explanation
The only days the Lion can say that he lied on the previous day are Mondays and Thursdays. The only days the Unicorn can say this, are Thursdays and Sundays. Therefore, the only day they both say that is on Thursday.

Merlin wrote, "OK, then. Since it is a stick shift, I'd say I could drive exactly zero miles."

As I have a cousin in Austin, I don't want any accidents so, in an effort to solve the riddle of the ?'stick shift' :

Starting the Truck
If it's not already so, put your car into neutral by pushing in the clutch and move the stick out of the gear gate. If you don't know what gate it is in, just tug the stick around until you feel it snap back into its neutral position (as in the center). Move the stick left and right to make sure you are in neutral. It should give easily. Are you still pushing in the clutch? Good. You can turn the key now.

Most new trucks require you to push in the clutch as you crank your engine because this will ensure that the car won't move anywhere when the engine is turning.The truck will have a failsafe in which if you try to start the truck without pushing in the clutch (even though you are in neutral), it will NOT even crank.

Moving the truck (in 1st gear)
The engine should be purring now. You can let go of the clutch at this point (provided that you are still in neutral). Assuming you are on flat land (empty parking lot, hopefully), lets get you going.

Push in your brakes and let go of your hand brake. Doing this will make sure you truck is not going to roll after you the hand brake is released (do this even on flat land JUST IN CASE!).

Push in your clutch ALL THE WAY DOWN.

*WARNING: This is important as most beginners push it in partially and not know it. Then when they try to engage to a gear, they will grind gears! Why does this happen? Because the engine is still turning and you are pushing a gear into a SPINNING engine! If you clutch it in all the way, the plates will be completely disengaged, which means the tranny is not at the mercy of the engine. This will allow you to put the tranny in gear without grinding it.

You can now put your truck in first gear. Let go of your brakes and immediately (be cool and casual about it, don't pounce!) push the gas a little while simultaneously releasing the clutch. The truck should move now. Jerky or not depends on how smoothly you released your clutch and how high the RPMs were. (Tip: Revving the engine just above 1000 RPM and letting the clutch go super slowly will let you feel how the truck will react). When you feel the truck about to move, you have found the cltuch's friction point. The two variables you have to think about is the clutch's engagement and the gas so the engine won't die. Too high of an RPM will launch your truck like a space rocket, so careful not to let go of the cluch fast (the term for that is "dropping the clutch") at RPMs of 3000 and above!

If the engine dies, don't fret. Try, try again! You will eventually get the hang of it. The reason why you may not be successful was probably because you didn't give it enough gas or you released the clutch to quick (though not to the point where you actually dropped the clutch).

Once you are moving, you can gradually give it some gas and let go of the clutch a little more until you have completely released the clutch. 1st gear have a pretty high ratio, so most likely, you should be shifting now. Although it's a preference, most people shift at around 3000 RPM. It depends on how the engine is handling it, really. If the engine can still take more (doesn't sound like it's huffing or puffing tired), you can shift a little higher. Others shift at around 2000 because we want to save gas (and we're the cheap breed!). Young drivers who drives fast (and want fast acceleration) shift near the red line. The term "red line" refers to the tachometer gauge in which the red zone starts (in you truck's manual book, it should say DO NOT rev beyond the red line... and you SHOULDN'T either!). That means these kids are maximizing the engine's potential, but of course, sucking up a lot of gas along the way.

To change gears, you must push the clutch in while letting go of the gas (simultaneously), then change the gear, and do the clutch-out-gas-in thing again. That's right...it's like a dance.

(Tip: To pass cars, you can't just hit the gas hard like you do in automatics. You must downshift (go to a lower gear), which will make your RPMs higher once you re-engage your clutch. This will allow you to do what the young kids do...accelerate quickly... to pass a car. Be warned, though - DON'T DOWNSHIFT IF YOU ARE ALREADY HAVE HIGH RPMs!!! Once you downshift, the RPMs will go higher than what you have already on your current gear, which will make the needle go PAST the red line, and blow your engine).

If you are not sure how to stop, take your laptop in the cab and post a ?'HELP' message. I will get back to you ASAP. :wink:

Will this help wizard work better than Microsoft's? I can just see it:

Are you having trouble a) starting the vehicle, b) changing gears, c) stopping.

Have you pressed the brake pedal?
Have you shifted to a lower gear?
Have you tried creating a sail out of your shirt to increase wind resistance?

I like your explanation, though. I've tried to teach my sister-in-law how to drive a stick. She does great when there isn't any traffic, but gets freaked out that people will yell at her if she stalls the car.

Merlin playing his part in environmental safety writes:

"Have you tried creating a sail out of your shirt to increase wind resistance?"

Ever since man changed from square wheels to round to REDUCE wind resistance. That is the problem. Keep your shirt on.


Whim, "Here you see 10 matches" (Safety type, I hope it is dangerous to play with matches) :wink:


At first glance, what you ask appears impossible. Nice one.

Whim,

To make sure I understand, is this the task?

- Start with what you have shown
- Each turn, one match is moved (not removed or added)
- The starting configuration for each turn is the ending configuration for the previous turn (as opposed to starting with what you have shown each time)

Yep that's it.

And no use of brackets. Calculation from left to right.

Whim

Whim, that was mind blowing. I hope I understood correctly. Great puzzle.

"A mind once stretched by a new idea never regains its original dimensions."


X-X X-X (=0)
VIII-VII (=1)
VII-V I-I (=2)
X-IV-III (=3)
V+IV-V (=4)
V+II-I-I (=5)
X-IX+V (=6)
V+V-III (=7)
VI-1+111 (=8)
V-V+IX (=9)


1. No Gentiles have booked noses;
2. A man who is a good hand at a bargain always makes money;
3. No Jew is ever a bad hand at a bargain.


1. All ducks in this village that are branded "B", belong to Mrs. Bond;
2.Ducks in this village never wear lace collars, unless they are branded "B"
3. Mrs. Bond has no gray ducks in this village.


1. All the old articles in this cupboard are cracked;
2. No jug in this cupboard is new;
3. Nothing in this cupboard, that is cracked, will hold water.

Whim, "…the plus sign are matches too"

Example:

||-|-||+| 0
|+|-||+| 1



Sorry to be so sloooow but, all my answers including + and - did = 10 matches.

X-X X-X (=0)
VIII-VII (=1)

However, I do see I failed to follow, "replacing just one match each time"

A person with a booked nose always makes money.
No gray ducks in this village wear lace collars.
No jug in this cupboard will hold water.

26 balls
360 containers

The balls are randomly divided over the containers.
A container can have more than one ball.
How many containers have balls in them according to probability?

Can you show me a formula, how to calculate this?

Mark writes:

A person with a booked nose always makes money.
No gray ducks in this village wear lace collars.
No jug in this cupboard will hold water.

A pleasure to read your answers.

Whim, Re - 26 balls / 360 containers. Does it matter how the ?'randomness' is achieved?
BTW I will re-visit your last set asap.

Something for the weekend. Don't answer too quickly as I am out and about. Have a good one.


1. All unripe fruit is unwholesome;
2. All these apples are wholesome;
3. No fruit, grown in the shade, is ripe.


1. Puppies, that will not lie still, are always grateful for the loan of a skipping-rope;
2. A lame puppy would not say "thank you" if you offered to lend it a skipping-rope;
3. None but lame puppies ever care to do worsted-work.


1. No name in this list is unsuitable for the hero of a romance;
2. Names beginning with a vowel are always melodious;
3. No name is suitable for a hero of a romance, if it begins with a consonant.



easy-to-tricky loids

101 D - 101
3 B M - 3
T 10 C - The 10
366 D I A L Y - 366 days
T 39 S - The 39
6 W O H T E - 6 wives
A B A T 40 T - Ali
T 7 W O T W - The 7
50 W T L Y L - 50 Ways
N 10 D S - Number 10
12 S O T Z - 12 signs


The problem :
Consider two cans, the first containing one liter of milk and the second containing one litre of water. Suppose you take one cup of milk out of the first can and pour it into the second can. After mixing you take one cup of the mixture from the second can and pour it back into the first can.

Which one of the following statements holds now?

The Solution :
There is as much water in the first can as there is milk in the second can.

An Explanation
In the end, both cans contain again one litre of liquid each. So the amount of milk that is replaced by water in the first can (which is somewhat less than one cup!) equals the amount of water that is replaced by milk in the second can (it is just an equal exchange).

The question :
Can you supply mathematical proof

101 D - 101
Cruella D'eville

3 B M - 3
See how they run

T 10 C - The 10
Moses

366 D I A L Y - 366 days
February 29th

6 W O H T E - 6 wives
Herman and the Hermits

A B A T 40 T - Ali
Open Sesame

50 W T L Y L - 50 Ways
Paul Simon

N 10 D S - Number 10
2800 Pensylvania Avenue

12 S O T Z - 12 signs
What's your sign?

Don't think so.



I'll await your answers. :wink:


whim

Merlin, thanks for a good laugh. Far better answers than I have.


26 balls
360 containers


n= the number of balls.
P(2) = the probability that at least two balls in container.
P(D) = the probability of no matches.

Theory: Using this terminology, probability theory states
P(2) = 1 - P(D).
Also, if an event is made up of several sub-events, then the probabilities are multiplicative.
That is, the probability of the event D can be found by multiplying the sub-events( a,b,c,...)
leading to event D
P(D) = P(a).P(b). P(c). …


In order for event D to occur, sub-event a must occur AND sub-event b must occur AND sub event c must occur AND so forth. Multiplying the probability of the sub-event will give us the probability of event Z occurring. The probability of the each sub-event is less than one. Each time you multiply numbers less than one, the result is even smaller yet.

Procedure: Calculate P(D).
P(D) = the number of ways that no ball matches, divided by the number of ways that they can be matched.

The denominator of P(D) is 360n. since that is the total number of containers.
In the numerator, we must consider how many ways containers can be distributed to n balls so that there are no matches. The first ball can fill any one of the 360 containers without restriction (with 360 ways out of 360 containers).


This means for two balls, the probability that they have different containers is
P(D) = (360) (359) = (360)(359) = 0.9973
and: P(2) = 1 - 0.9973 = 0.0027

For n balls
P(D) =
(360)(359)(358)….(360 - (n-1))
360n
and: P(2) = 1 - P(D).

Which leaves us with:

26 balls
0.5982 (or thereabouts)

Adapted from ?'Birthdays in a room'. :wink:

None of these apples were grown in the shade.
Puppies that will not lie still never care to do worsted-work.
All names in this list are melodious.

T 39 S
The 39 Steps

T 7 W O T W
The 7 wonders of the world

WATER/MILK

Let W represent one unit of water
Let M represent one unit of milk
Let C represent the capacity of the cup (0 <= C <= 1)
Let D represent the number of units of water that get transferred in the second transaction (0 <= D <= C)
The number of units of milk that get transferred in the second transaction will be C-D.
Note that I'm not assuming that the milk and water mix perfectly after the first transaction.

26 Balls
360 Containers

Here are the probabilities that the balls are contained in exactly N containers.
For B balls and C containers, the generic formula is
C(C,N)*C(B-1,B-N)/C(B+C-1,B)
C(x,y) = x!/[y!(x-y)!] = # combinations of x things taken y at a time
The formula for this situation is C(360,N)*C(25,26-N)/C(385,26)

How many containers have balls in them according to probability?

13?


whim

Mark, award yourself a blueberry muffin.



None of these apples were grown in the shade.
Puppies that will not lie still never care to do worsted-work.
All names in this list are melodious.

T 39 S
The 39 Steps

T 7 W O T W
The 7 wonders of the world

WATER/MILK

Your answer works for me.


I have:

Let the cup have contents c.
We start with 1 litre of milk and 1 litre of water:
first can: second can:
1 milk 0 milk
0 water 1 water
We take one cup of milk, pour it into the second can, and mix it. The result is:
first can: second can:
1-c milk c milk
0 water 1 water
The concentration of milk in the second can is c/(1+c); the concentration of water in the second can is 1/(1+c). We now take one cup of the mixture in the second can and pour it back into the first can. This cup contains c x c/(1+c) milk and c x 1/(1+c) water. The result is:
first can: second can:
1-c + (c x c/(1+c)) = 1/(1+c) milk c - (c x c/(1+c)) = c/(1+c) milk
0 + (c x 1/(1+c)) = c/(1+c) water 1 - (c x 1/(1+c)) = 1/(1+c) water
So now there is as much water in the first can as there is milk in the second can.



Whim asks, "How many containers have balls in them according to probability?"

The answer to which I missed in my answer. Nevertheless, my conclusion is that there is a better than 50% chance that at least one container will have two balls.

I note Marks answer. However, I am somewhat confused by the last line: 26 = 0.164134697

Over to you Whim for your comments.



Imagine you are on an island called Exel, with inhabitants that look the same from the outside, but differ from inside (their truthfulness). We distinguish the following types:

Knights, who always tell the truth.

Knaves, who never tell the truth.

Normals, who sometimes tell the truth and sometimes lie.

Assume you meet one of these inhabitants, and he tells you: "I'm no Knight". Then, what type is the inhabitant


1. All members of the House of Commons have perfect self-command.
2. No M.P., who wears a coronet, should ride in a donkey-race.
3. All members of the House of Lords wear coronets.


1. No goods in this shop, that have been bought and paid for, are still on sale.
2. None of the goods may be carried away, unless labeled "sold".
3. None of the goods are labeled "sold" unless they have been bought and paid for.


1. No Acrobatic feats, that are not announced in the bills of a circus, are ever attempted there.
2. No acrobatic feat is possible, if it involves turning a quadruple somersault.
3. No impossible acrobatic feat is ever announced in a circus bill.