Chester has a RED dot and here is his thinking...

If I had a BLACK dot on my forehead and since all 3 of us have raised our hands, it is evident that both Rob and Mike will see just one RED dot (on the others forehead) and should immediately realize that they have a RED dot on their own forehead. Since they have not realized this yet, I must have a RED dot on mine too!

If the above explanation is not obvious, think about it this way. If there were only one RED dot, only 2 of the 3 would have raised their hands. So, there are at least 2 RED dots. If this was the case, and Chester's was BLACK, one of the other 2 would be able to conclude that his own has to be RED, since he sees only one RED. Since this has not happened (silence!), then it must be the case that all three are REDs.

Hope this will do it!

How do you know before the birth of Christ that the event will occur in 7 years?

In a Dictionary?

Silence

The street was (one way),that means,he can not drive close to the entrance and wait to see weather it is possible or not....cause there are another cars on the road.

Well, in that case it is back to the Marlboro I guess! See, I tried my best to stay away from the "cigarette" - as far as possible - not only an arm's length!

From the problem statement, there is no way we can measure the height of the tunnel throughout its entire length! So, all we are trying to measure is the height at the entrance of the tunnel. In that case, isn't is just simpler and more practical to drive as close as possible to the entrance (without getting stuck, of course) and use eye estimation at that point? All this trigonometry stuff with a cigarette held at arms length and no other measuring tools will give a very rough order of estimate anyway.

\ /

\/

(4 slashes making 5)

A family of 4 with a pregnant mom will soon be 5

The priest who responded did know the answer to the great question, so he has to be a knave (as per conditions in the first part of the problem).

Since he is a knave, the drastic conclusion to the Great Question must be :

"There is Nothing instead of Something!"

I'm glad this little puzzle tickled as much

interest that it did! It really seems counter

intuitive. Congratulations to EventHorizon

for his quick correct response. For a problem

where accuracy is paramount, he got the height

right on the nose. Thank you to everyone who

worked on it.

Thanks Superprismatic for a wonderful puzzle!

Let

r be the radious of tha sphere.

y be the distance from the ground to the top of where you pull the rope

a be the angle from where you stand to where the rope is tangent to the sphere

x be the distance from where the rope is tangent to the earth to where you are pulling the rope

tan (a)=x/r

hence

x = r*tan(a)

2*pi*r - 2*a*r + 2x = 2*pi*(r+1)

substitute x

2*pi*r - 2*a*r + 2*r*tan(a) = 2*pi*(r+1)

2*r*tan(a)-2*a*r=2*pi

a~~0.6528°

We also know:

r^2 + x^2 = (r+y)^2

substitute x = r*tan(a)

r^2 + (r*tan(a))^2 = (r+y)^2

solve for y

y ~ 413 m

In the following step:

2*pi*r - 2*a*r + 2x = 2*pi*(r+1)

How are you getting the (r+1)? 1 meter was added to the circumference, not the radius.

Going by all the posts so far, I think EventHorizon deserves a BIG round of applause for keeping a cool head and going through the calculations properly. I agree with him that even a small rounding error will result in a big difference in the solution.

Made a stupid mistake in my hurry. No wonder the result was ridiculous!

Eventhorizon's solution checks out all right! Good work.

A quick calculation results in 1,346,596 meters. Definitely need to check this once more. But, I have to leave now...

Exactly what I said, but in better wording.

You are correct Aaryan!

Neither a Knight nor a Knave can make the stand-alone statement "I am a Knave!" That would lead to a paradox. However, a Knave could very well make the statement "I Am a Knave" if it is "AND"ed with any other statement which is false. A Knight could never do that because both parts of his statement would have to be True.

So, the first priest is a Knave and by above logic he does know why there is something instead of nothing. I am sure if you stay with him a while you would also be able to know the reason in spite of the priest being a Knave. For, as we all know, a Knave is as good as a Knight since we know exactly what sense to make of his statements!

The car was being towed and the man died at a hospital!

u4472b0

Yes.

Though the answer to the question is 'Yes', it is not the answer given by the inhabitant asked. As a Knight would answer "Yes" regardless if his companion were a Knight or Knave, and a Knave would also answer "Yes" if the other resting inhabitant were a Knave, the answer received must have been "No", with the answerer being a Knave and his companion being a Knight. Nevertheless, the answer is 'Yes' because 'I can tell.'

Good one - Dej Mar!

"No" or "Neither of us" which means he is a Knave and the other is a Knight. This is the only option if the answer is negative.

Had he answered affirmatively there are 3 possibilities: Both are Knaves, or the person answering is a Knight and the other is either Knight or Knave. Since the question states that from the answer given you can determine the character of both persons, the answer must have been "no".

Copernicus - You nailed it! Couldn't have explained it better.

"just_tonight" and "thirdtimescharm" were also correct in their answers but were only lacking in a thorough explanation.

Have a good weekend everyone!

Knave while the other was a Knight. You know because he could not have been telling the truth when he answered "No."

Please note that I did not disclose what the answer was. BTW, these type of puzzles are sometimes called "meta-puzzles" since it seems like not enough information is given. But, in fact, they can be solved!

This is an easy one for Friday...(I searched for this one but couldn't find it in previous posts)

While on the land of Knights (people who always tell the truth) and Knaves (people who always lie), I came across two inhabitants resting under a tree. I asked one of them, "Is either of you a Knight?" From his answer I immediately knew what kind he was and also what the other guy was. Can you tell?

The statements are inconclusive and do not lead to a specific solution. However, if we assume that X is a good door, we do not land up with any obvious contradictions. So, that, at least, is a correct answer.

Since a "cousin" is defined as a relative with whom you share a common ancestor (or ancestors),the two boys would be "cousins" - OR if you prefer, the even more generic "blood relative"

The side of the board since it is at least visible. The back of the board is another option but that would be "unfair".

3125

2,3,4,5 raised to the power of 2,3,4,5!