Puzzle Post

Mandle · Sat 12/09/2015 16:12:31

Post your puzzles here on the Puzzle Post:

And I see no reason why multiple puzzles/lateral thinking riddles/etc. cannot exist side by side at the same time as long as the potential solvers of said puzzles make it clear which one they were replying to.

Here is a starter-off and probably the best puzzle I have ever encountered in my life.

I'm not sure how famous this puzzle is so if you already know the answer please do the respectful thing and leave it to those who have not already had the enjoyment of figuring it out to...figure it out...

Four people are in a room, labelled A,B,C,and D...

Each wear either a black or a white hat, as shown in the illustration below:

[imgzoom]http://i28.photobucket.com/albums/c201/Mandle/BestPuzzle01_zps5jbqjiv6.png[/imgzoom]

Each person faces to the left.

Each person cannot see the colour of the hat they are wearing.

Each person knows their A,B,C,D order, meaning that they know how many people are in front of them and how many are behind them.

All of the people know that there are 4 people in the room.

All of the people know that there are 2 white hats and 2 black hats.

They are not allowed to turn around or speak to each other.

The black bar labelled W represents a wall dividing the room which cannot be seen through, nor is it a mirror (no cheap tricks like that).

A can only see the wall right in front of them.

B can only see the wall right in front of them.

C can see the colour of B's hat.

D can see the colour of B's hat and C's hat.

The object of this puzzle is to determine which person will first correctly and with 100% certainty be able to say if they are wearing a black hat or a white hat, and also be able to explain how they knew.

SO:

Which person knew the colour of the hat they were wearing and how did they know?

(Please hide answers so that others may have a fair go at the puzzle with no spoilers)

Cuiki · Sat 12/09/2015 16:26:10

Spoiler

Is it person C, because he knows that if he was wearing a white hat, the person behind him would be able to tell the colour of his own hat right away?

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Stupot · Sat 12/09/2015 19:22:26

Spoiler

Yeah I'm with Cuiki.
I will give a deeper explanation.

Spoiler

Don't look if you haven't already had a good go at working it out.

Spoiler

Seriously, have another go.

Spoiler

If C were wearing a white hat then D would have seen two white hats in front of him and announced he's wearing black. But D won't have said anything, so C can work out that D must be seeing one black hat and one white hat. And since he know's that B's hat is white, his own must surely be black.

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Nice puzzle. We've had similar threads before and some variations of these hat puzzles came up but I don't think this particular version with the wall came up, so nice one.

Cuiki · Sat 12/09/2015 22:09:31

Well, I think I'll let someone else come up with the next one.
Unless you'd like to be bored to death with my probability puzzles...

Mandle · Sun 13/09/2015 00:30:03

Cuiki & Stupot are both correct of course. Well done! As with all great puzzles as soon as you find the correct answer you already know it to be correct without having to be told so.

But I urge you to try this puzzle out yourself and give it a decent try before looking at their answers. There is a real sense of satisfaction from solving it.

Quote from: Cuiki on Sat 12/09/2015 22:09:31
Well, I think I'll let someone else come up with the next one.
Unless you'd like to be bored to death with my probability puzzles...

I think for this thread it's best if anyone can just post up a puzzle at any time, even if there are multiple puzzles running at the same time. Puzzles that are not ridiculously well-known already are quite hard to come by so I think the winner-posts-next-puzzle format will not work very well.

I have one of my own devising. It's probably not all that great but at least it's ungoogleable:

A man gets out of the way of a fast-moving car just bare seconds before it would have hit and most likely killed him, and yet he is not in the slightest bit shaken-up by the experience. The man was aware of the vehicle (he's not blind etc.), he's not drunk or on drugs, and he is not a professional stuntman or anything like that.

What's the reason for his cool demeanor?

The answer is not based on word-play or puns within the question etc. What you see is what you get. Hide answers please.

Baron · Sun 13/09/2015 05:00:21

Spoiler

Er.... he's crossing a busy street? Daily pedestrian fatalities in major urban centres suggest he would be nonplussed by the velocity of the traffic heading towards him: otherwise, how can you account for their unnecessary risk taking?

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Mandle · Sun 13/09/2015 07:06:12

Quote from: Baron on Sun 13/09/2015 05:00:21
Spoiler
Er.... he's crossing a busy street? Daily pedestrian fatalities in major urban centres suggest he would be nonplussed by the velocity of the traffic heading towards him: otherwise, how can you account for their unnecessary risk taking?
[close]

100% correct...yeah...like I said...it's probably not that great a puzzle...

SPOILER ALERT:

Spoiler

We all feel cars pass by just behind us when crossing a main road and hardly think twice about how close we just came to death...

So the moral of this puzzle is: STAY SAFE GUYS!!! And never assume that the person driving the car is not typing on their pho...

OH SHIIIIIT!!!!....

(Phew...that was a close call...)

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Mandle · Sun 13/09/2015 07:39:13

Which way is the bus moving?

A or B?

And why?

(hide answers)

Cassiebsg · Sun 13/09/2015 08:51:39

Spoiler

Depends on which country you are.

A in any country that drives on the right side, B in all other countries that drive on "the wrong side".

Spoiler

Why? Cause all you can see are windows, so door is on the other side.

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Mandle · Sun 13/09/2015 09:16:29

Quote from: Cassiebsg on Sun 13/09/2015 08:51:39
Spoiler

Depends on which country you are.
A in any country that drives on the right side, B in all other countries that drive on "the wrong side".
Spoiler

Why? Cause all you can see are windows, so door is on the other side.
[close]
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Yup...It actually doesn't matter if you choose A or B as long as you are able to explain why...

And you nailed it!

Mandle · Sun 13/09/2015 09:35:02

Alec and Alexia grow carrots.

Carlo and Clover grow oranges.

Paula and Phillip grow apples.

Michael and Michelle grow what?

Gurok · Sun 13/09/2015 09:39:30

Spoiler

Lemons

[close]

Spoiler

Last letter of their first and surnames = First two letters of each fruit/vegetable

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Mandle · Sun 13/09/2015 09:45:25

Quote from: Gurok on Sun 13/09/2015 09:39:30
Spoiler
Lemons
[close]

Spoiler
Last letter of their first and surnames = First two letters of each fruit/vegetable
[close]

Correct!

Give me some time...I'm gonna think up a puzzle that has never been done before...

I might need some time...Like Deep Thought needed some time...

In the meanwhile please post your own puzzles...

Crimson Wizard · Wed 16/09/2015 13:58:03

Here is one interesting numbers puzzle I was told about by my math teacher.

Code: text


1
11
21
1211
111221
312211
13112221
1113213211
31131211131221

What is the next number?

This may be considered a hint, so I hide it under spoiler:

Spoiler

According to his story, this puzzle was introduced at some mathematician symposium and caused quite a ruckus when it was found that big mathematicians could not solve it

.

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Sinitrena · Wed 16/09/2015 15:26:41

Spoiler

13211311123113112211

[close]

Spoiler

In the first line is one "1" - that means line 2 is "11"; in line 2 are two "1" - so line 3 is 21; in line 3 is one "2" and one "1" - 1211 - and so on.

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Crimson Wizard · Wed 16/09/2015 18:29:27

Sinitrena is correct.

Sinitrena · Thu 17/09/2015 15:56:26

How about an easy one?

A book has 973 pages, numbered consecutively from 1 to 973. On every page is just a single sentence. On page 1: "There is exactly one false statement in this book." On page 2: "There are exactly two false statements in this book." And so on: On every page there is a single sentence stating that there are exactly as many false statements in the book as the page you are on.
Is there a page that tells the truth and if yes, which one?

Crimson Wizard · Thu 17/09/2015 16:12:49

Quote from: Sinitrena on Thu 17/09/2015 15:56:26
A book has 973 pages, numbered consecutively from 1 to 973. On every page is just a single sentence. On page 1: "There is exactly one false statement in this book." On page 2: "There are exactly two false statements in this book." And so on: On every page there is a single sentence stating that there are exactly as many false statements in the book as the page you are on.
Is there a page that tells the truth and if yes, which one?

Well, I guess

Spoiler

It is page 972 that tells that there are 972 false statements in this book.

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Sinitrena · Thu 17/09/2015 16:33:55

Correct.

Wyz · Thu 17/09/2015 16:44:50

Spoiler

CW is correct. The logic behind it:
There can be at most one statement correct: if there were two or more they would always contradict each other.
Assume there was no correct statement then there would be 973 false statements. This is exactly what the statement on page 973 says. But this statement would be true then so this contradicts.
Assume there is one, then the other statements would be false so 973 - 1 = 972 statements would be false. This is exactly what the statement on page 972 says.
This is the correct answer.

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Edit: too late