The worlds first riddle!

The following table lists the steps:

Starting Bank The Boat Finishing Bank
HHHEMM
HHHM EM
HHHM E M
HHH EM M
HHH E MM
HE HH MM
HE HM HM
HM HE HM
HM HM HE
MM HH HE
MM E HHH
M EM HHH
M E HHHM
EM HHHM
HHHEMM


Not lost again.

While crossing the desert, you become lost in a sandstorm. After wandering for days, your water supply nearly exhausted, you come upon an oasis. With plenty of fresh water and edible flora about, you replenish your supplies and contemplate your situation.

You know from experience that you can carry about three days worth of water and food. Your most efficient walking pace covers about twenty miles in a day. You have an accurate compass, so you can travel in a straight line, but you don't know where you are. Fortunately, you know that no part of the desert is more than a hundred miles in any direction from civilization.

Two questions:

a)How quickly can you guarantee escape from the desert

b)If the desert was more than a hundred miles in radius, what's the furthest you could travel given unlimited time

Assume that the oasis has unlimited supplies, you can always find any supplies you drop along the way, and that you can drop water and food in arbitrary amounts.

You can get all 100 feet of rope and you don't need the pocketknife.

The desert one sounds very similar to the rocket one somebody posted the other day. There the answer was 15 days but in this one you can place your supply bases anywhere you want. Hmmm will have to think.

The answer to part b) is infinite.

The first part is confusing.



So this is not radius 100 miles is it? It's diameter.
Very different answers depending which you mean.

OK, full solution for the rope one.

1. Climb up one of the ropes and untie the knot in the other one allowing it to fall to the floor.

2. Tie the ropes together giving you 100 feet hanging from one ring. NOTE: MAKE SURE that the knot is small enough to pass through the ring without fouling.

3. This is the hard part. Now you have to tie the loose end of the rope into a harness around your waist and climb up to the top again.

4. Hang from one ring while untieing the rope from the other. NOTE: DO NOT let the rope fall or you're buggered.

5. Thread the rope through the ring. This makes a basic pulley that you can use to lower yourself back to the ground.

6. You now have a 100 foot length of rope to tie around the bars in the window. Abscond at your leisure.

a) Your American measures always confuse me
b) Depends : DC - some time, depends - but always slower than speed of light. AC - never..
c) Deceiving. VERY. As in the cars problem.
d) Huh, I need a navigator over Pacific.
e) Moon
f) no.
g) Oko, uho, las, rit, kri, arm, leg, lip, toe, rib
h) Besides being listed in your sentence?
i) Light, sound, pain (depends on you attention & reflexe)
k) Easy for Civ players

Concernig the old 'probability' puzzle:
"If he was opening a random door then it would not make any difference, it would be 1/3 of the time either way because 1/3 of the time he would open the curtain with the car. "
If he was opening a random door, your probability would be 50-50 after seeing an empty space. It would be 0-0 after seeing a car.

It is interesting that if you don't actually know if the man uses random or not you can't decide correctly - to switch or not (it does not hurt if you switch - since it is 50-50 in random case. But imagine he is always choosing a 'full' curtain on purpose only showing blank when you already chose the car? In this case you must not switch!)

With the old problem, I think I am right in saying he always opened an empty curtain. You must be right with the odds. 1 in 3 to start. Then 1 in 2 with the one open curtain.

Anyway, this riddle contains no weights.

What do you know about, conditional probability'? Easy question difficult answer.

You are lost in the woods. You come to a T-junction and are wondering which way to go. You have a funny feeling that one way will get you out, the other will mean certain death. Weird, eh?

A pixie approaches you.

"A left turn will get you out of the woods," it advises.

A nearby sprite hears this and calls out, "Beware of him. He lies!"

"Exactly 4 times out of 10, I do!" the pixie retorts, and disappears.

You know from folklore that all sprites always tell the truth. You also know that throughout their life, an individual pixie tells the truth a certain number of sentences out of ten, determined by chance at birth. You also know this number is an integer.

Which way should you turn to maximise your chance of escape, and why



Oh, No. Not still lost?

Lost in the forest, you come across a clearing that diverges into 3 roads. There is a cabin here, and, not knowing which road to take, you knock on the door hoping to find the correct path out of the woods.

An old man answers and says that, while he no longer remembers the trails, maybe one of his children can help you. The old man says that out of his ten children, 5 of them always tell the truth and 5 of them always lie. However, he also adds that only 5 of them actually know the correct path.

Each child knows what type of child each of the others is, and what knowledge they possess. The ten children are lined up, and you ask each of them separately which road to take: the left, middle, or right. While each child whispers his answer to you, it is still loud enough that the next person in line can overhear what they said.

The ten replies were...

1) Take the left road
2) Take the right road
3) Don't take the middle road
4) Take the right road
5) Don't take the right road
6) Take the middle road
7) Don't take the left road
8) Take the left road
9) Take the middle road
10) Don't take the left road

Which road is the way out

Words ending in 'dous'

I query the fact that there are only four. 'Hazardous', and 'blizzardous', are perfectly good English words and I am sure there are others.

Three-letter body parts:
Arm, leg, toe, eye, ear, rib, gut, jaw, gum, hip, a$$, t!t, nut.

Three roads:
The right road

Hats of power:
C = red and alternates
A = blue and lies
D = green and is a mystic
B = black and tells the truth.

Waterlilies:
I wrote a while back that 'Monet clinched it for me'. That seems to have gone right past you, Try, so I guess I am being too smart for my own good again.

Try

Either your 'hats of power' is not the hardest puzzle you have posted or I was fortunate to stumble on the right approach. It took me no great length of time and, for sure, that has not always been the case with all of your puzzles

I have sent a pm with my proposed solution to the 'spy' puzzle.

The 'a to k' list of questions:

a) Gold would be heavier as precious metals are weighed in Troy ounces, lead in ounces Avoirdupois. (And I agree fully with Relative about non-metrical units of measurement)

b) No precise figure but it would take surprisingly long. For example, the average snail would get there faster.

c) A tricky one. At first sight I was prepared to argue that the answer should be 'evens'. Only later did I realise/calculate that it would be one-in-three.

d) and e) Relative has already answered.

f) facetiously

g) I have answered this one elsewhere.

h) No idea, but I figure that variation in taste - i.e. a wide selection - has something to do with it.

i) This question is ambiguous with no clear answer. The light stimulus would reach the brain first, the sound second, the pain third. However, the first two could mean anything (and could well go unperceived). Only the pain would - possibly - say for sure that this is an attack. So only the pain would be 'evidence of an attack', the others would be, if evidence of anything, merely evidence of a flash of light and of a bang until connected with the injury.

j) What is a Star Trek?

k) Not without a lot of trawling through my brain, if then.
I would argue that this is an arbitrary list and it has changed more than once. Also, it is difficult to take a list seriously that does not include Asia or the Americas, where there are some astonishing ancient constructions. The Great Wall of China is not a wonder? Ptooie!

h) Music they sent up on Voyager.

i) You would hear it before you felt it.

k) Moby Dick.

Adrian

Sure you'd hear it before you felt it. And you'd see it before you heard it. But the question referred not to knowledge in general but 'evidence of an attack' and an attack, by definition, is not a flash of light or a loud bang.

Okay, here are the answers.

a) The 18 ounces of gold weigh substantially more than the 18 ounces of lead. Unlike the classic "pound of feathers vs. pound of bricks" trick, there is a difference- not in physics but units. Gold is commonly measured in troy ounces which is 31.103 grams metric. This is compared to a normal (avoirdupois) ounce which is 28.350 grams.


b) Several hours: While electrons travel at close to the speed of light, their path inside the wire is not direct. The electrons are constantly bouncing off each other. So while the electricity completes the circuit instantaneously, an individual electron takes a very long time. Related would be a photon generated near the centre of the sun- it might take close to a million years to reach the surface of the sun, and another 8 minutes to get to the Earth.


c) Assume the four cards were the four queens: there are two ways of getting the same suit: QS/QC and QH/QD, while six total possible combinations. So one in three.


d) The Pacific Ocean. Most of us accustomed to Mercator projection maps think of North America being more or less lined up directly above South America, but look on a globe and see that almost all of South America is east of North America.


e) The moon. (groan...)


f) There are two: facetiously and abstemiously.


g) Ear, eye, arm, toe, lip, leg, gum, hip, jaw, rib.


h) They were all on the first album to go "trans-solar", on Voyager.


i) If you happened to be looking straight at him, the flash from his rifle would reach you almost instantly. Assume for a moment that the he is a competent assassin who hid himself well (and for some reason was aiming for your foot). The speed of sound is approximately 1129 feet per second at sea level. The sound will reach your ears in .044 seconds. The bullet will hit your foot in .038 seconds. So much for dodging the bullet on this one. But I asked which would be the first evidence to you- and that would be the sound. Because once the bullet hits your foot, the pain impulse must travel your myelinated A-fibers to your brain at 330 feet per second. Assuming you're five feet tall, that's an extra .015 seconds onto the trip.


j) Captain Ahab, from Melville's "Moby Dick".

k) The Pyramid of Giza, The Gardens of Babylon, The Lighthouse of Alexandria, The Colossus at Rhodes, The Statue of Zeus, The Temple of Artemis, and the Mausoleum at Halicarnassus.


If you got eight or more of these questions right without using outside sources, you can consider yourself a master Riddler. If you got twelve, I don't believe you! :wink:

Congratulations to Adrian, Lacomus and Relative for ALL the correct answers.

Try this:

In the quiet village, almost every man is completely faithful to his wife. Why? Because, all the men are honourable gentlemen. Slightly germane as well is the long-standing tradition that if a woman ever learns her husband is unfaithful, she will kill him that night while he sleeps.

It also may be relevant that the women are notorious gossips. If a woman discovers a man to be untrue, either on her own or through heresy, this fact will quickly be known throughout the village within a matter of hours to all the married women except the wife of the unfaithful man.

One fateful day a fortune-teller came to town and revealed the terrible truth: some man or men had been unfaithful.

For a week, a great fear gripped the town as every woman wondered if her man was true, and as every philandering man wondered if his days were numbered.

Then, on the eighth morning after the fortune-teller came, the coffin maker received his orders. How many men were dead



China has been grappling with a population problem for some time.
For numerous social and cultural reasons, families strongly prefer male children to female.

Consider a hypothetical city somewhere in China where the practice has arisen that every family continues to procreate until a son is produced, at which point they stop having children.

Assuming that boys and girls are born with equal probability, what is the ratio of boys to girls after 100 generations


Simple riddle. (Part 1)

If you fear that I am near,
Here's a wise word in your ear,
You may look forth and aft for me,
But to do so simultaneously,
Ensures you'll just look straight through me,
Even if I'm right behind thee.

What am I

Finally I got some time for the ten brothers puzzle.. and solved it quicker than I thought.

You'd best take the MIDDLE road.

Relative

About the pixie : I'm no expert in conditional probability, but i'd say it is more likely that this pixie lies than not. I'd say this because he cannot tell 0 lies out of ten (the sprite told you so), which would be required to balance that he could be telling 10 out of 10 lies. Ergo, it is more likely that the right road will save you. Concerning his self-referential statement (that he lies 4 times out of 10) i believe it is not relevant at all. We can only say it is more likely to be a lie than not - but we cannot get any info out of it.

Does this make any sense ?

Relative, you 'win' again

Take the middle road.

If you break down the 10 answers, you have 2 people telling you to go right, left, and middle. You also have 2 people telling you NOT to take the left. Therefore, left cannot be the correct answer because 6 people would be lying.

To decide whether to go right or middle, you must determine how many children MUST have known the correct road ahead of time for each case. Remember, 5 children do not know the correct path, but can determine what to say or not to say by overhearing the child before them.

If the correct road is right, then children 1,5,6,8,9 are lying and children 1,2,4,7,9,10 (6 children) must have known the correct path without help from someone else.

The correct road is the middle, since only children 1,2,3,6,9 needed to know the road. The statements given by 4,5,7,8,10 can be deduced from the child's statement preceding them.


The solution to the Pixie problem is found through conditional probability.

To begin with, there are 11 possibilities for the number of times out of 10 the pixie lies. For each of these possibilities, find the probability that the pixie would be able to make the statement "I lie exactly 4 out of 10 times." For example, in the case that the pixie actually lies 7 of 10 times, there is a 7/10 probability that he is able to make the (false) statement "I lie exactly 4 out of 10 times."

The probability of the pixie being able to make the statement is the same as the probability of the pixie lying, except for the case that he is telling the truth (4/10); in that case, the probability of him being able to make that statement is 6/10 (which is equal to the probability of him being able to make a true statement).

Now, conditional probability says that the probability of the pixie lying X number of times out of 10 in his life is equal to the probability of him being able to make the statement (X/10, unless X is 4) divided by the sum of probabilities for all the cases. So, for our example, the probability that the pixie tells lies 7 of 10 times is:

(7/10) / (0/10 + 1/10 + 2/10 + 3/10 + 6/10 + 5/10 + 6/10 + 7/10 + 8/10 + 9/10 + 10/10) = 7/57

Similarly, the probability that the pixie lies X of 10 times is:

X/57, for X not equal to 4,
6/57, for X equal to 4.

Now we can find the probability of the pixie lying in his first statement. There is a X/57 chance (or 6/57 for the 4 of 10 case) that the pixie lies X of 10 times, and for each of these cases there is a X/10 chance that the pixie lied about the path. To find the odds that the pixie lied, simply add the products of probabilities for each case:

0/570 + 1/570 + 4/570 + 9/570 + 24/570 + 25/570 + 36/570 + 49/570 + 64/570 + 81/570 + 100/570 = 393/570 = 68.947%.

So, the probability the pixie lied is 68.947%, and you should go right.

Relative, your reply did answer the question.

The correct road was the middle road.

I said 'the right road'.

Sure enough, child 5 must have told the truth thus eliminating 'right'.

If only I could see where I went wrong as easily before I posted as I can after someone has told me the right answer