Riddles and Puzzles

[classic33]

I Am Not
Nestled perched upon my cliff
On either side the herd doth stream
At wat'ring hole they catch my whiff
The starving beast craves blood supreme
I bear and bare a serpent's fang
Inflicting burn with venom dear
And thus my prey, away it sprang
My fire's roar it's sure to hear

What am I?

 

[classic33]

Arrange The Letters
How should the top set of letters be arraigned over the lower set of letters?
A B C D E F G
J F M A M J J A S O N D

 

[ianrauk]

A F C.......E...G....B....D
J F M A M J J A S O N D

As a guess

 

[classic33]

A F C.......E...G....B....D
J F M A M J J A S O N D

As a guess

Close, but No.

 

[classic33]

Uneqal Marathon!
Alice and Bob run a standard 26.2-mile marathon race.
Bob's pace is a constant 8 minutes/mile, start to finish.
Alice's pace is such that for every 1-mile segment of the race, she takes 8:01 minutes.
That is, between mile markers 10 and 11, Alice consumes 8:01 minutes.
And between miles 6.374 and 7.374, Alice consumes 8:01 minutes.

Is Bob the sure winner of the marathon?

 

[classic33]

Prisoners On Death Row
You are one of 20 prisoners on death row with the execution date set for tomorrow.

Your king is a ruthless man who likes to toy with his people's miseries. He comes to your cell today and tells you:

“I’m gonna give you prisoners a chance to go free tomorrow. You will all stand in a row (queue) before the executioner and we will put a hat on your head, either a red or a black one. Of course you will not be able to see the color of your own hat; you will only be able to see the prisoners in front of you with their hats on; you will not be allowed to look back or communicate together in any way (talking, touching.....)

(The prisoner in the back will be able to see the 19 prisoners in front of him
The one in front of him will be able to see 18…)

Starting with the last person in the row, the one who can see everybody in front of him, he will be asked a simple question:WHAT IS THE COLOR OF YOUR HAT?

He will be only allowed to answer “BLACK” or “RED”. If he says anything else you will ALL be executed immediately.

If he guesses the right color of the hat on his head he is set free, otherwise he is put to death. And we move on to the one in front of him and ask him the same question and so on…

Well, good luck tomorrow, HA HA HA HA HA HA!”

Now since you all can communicate freely during the night, can you find a way to guarantee the freedom of some prisoners tomorrow?
How many will win their freedom?

 

[nickyboy]

Prisoners On Death Row
You are one of 20 prisoners on death row with the execution date set for tomorrow.

Your king is a ruthless man who likes to toy with his people's miseries. He comes to your cell today and tells you:

“I’m gonna give you prisoners a chance to go free tomorrow. You will all stand in a row (queue) before the executioner and we will put a hat on your head, either a red or a black one. Of course you will not be able to see the color of your own hat; you will only be able to see the prisoners in front of you with their hats on; you will not be allowed to look back or communicate together in any way (talking, touching.....)

(The prisoner in the back will be able to see the 19 prisoners in front of him
The one in front of him will be able to see 18…)

Starting with the last person in the row, the one who can see everybody in front of him, he will be asked a simple question:WHAT IS THE COLOR OF YOUR HAT?

He will be only allowed to answer “BLACK” or “RED”. If he says anything else you will ALL be executed immediately.

If he guesses the right color of the hat on his head he is set free, otherwise he is put to death. And we move on to the one in front of him and ask him the same question and so on…

Well, good luck tomorrow, HA HA HA HA HA HA!”

Now since you all can communicate freely during the night, can you find a way to guarantee the freedom of some prisoners tomorrow?
How many will win their freedom?

During the night the prisoners devise a code. If they are even numbered in the queue (20th, 18th, 16th etc) they have to look at the colour of the hat of the person directly in front and call out that colour. This is the sign to the odd numbered prisoners as to what colour their hat is. This way P19, P17, P15, P13, P11, P9, P7, P5, P3, P1 all give the correct answer and are saved. Totalling 10 prisoners. The even numbered prisoners have called out either Red or Black and they have a 50/50 chance that their hat is the same colour as the prisoner immediately in front. Statistically, 5 of the even numbered prisoners should get this right and 5 get it wrong. Although of course in reality 0 may get it right or 10 may get it right.

So 10 are guaranteed to be saved with this method and the other 10 have a 50% chance of being saved too

 

[classic33]

During the night the prisoners devise a code. If they are even numbered in the queue (20th, 18th, 16th etc) they have to look at the colour of the hat of the person directly in front and call out that colour. This is the sign to the odd numbered prisoners as to what colour their hat is. This way P19, P17, P15, P13, P11, P9, P7, P5, P3, P1 all give the correct answer and are saved. Totalling 10 prisoners. The even numbered prisoners have called out either Red or Black and they have a 50/50 chance that their hat is the same colour as the prisoner immediately in front. Statistically, 5 of the even numbered prisoners should get this right and 5 get it wrong. Although of course in reality 0 may get it right or 10 may get it right.

So 10 are guaranteed to be saved with this method and the other 10 have a 50% chance of being saved too

No.

 

[Over The Hill]

Prisoners On Death Row
You are one of 20 prisoners on death row with the execution date set for tomorrow.

Your king is a ruthless man who likes to toy with his people's miseries. He comes to your cell today and tells you:

“I’m gonna give you prisoners a chance to go free tomorrow. You will all stand in a row (queue) before the executioner and we will put a hat on your head, either a red or a black one. Of course you will not be able to see the color of your own hat; you will only be able to see the prisoners in front of you with their hats on; you will not be allowed to look back or communicate together in any way (talking, touching.....)

(The prisoner in the back will be able to see the 19 prisoners in front of him
The one in front of him will be able to see 18…)

Starting with the last person in the row, the one who can see everybody in front of him, he will be asked a simple question:WHAT IS THE COLOR OF YOUR HAT?

He will be only allowed to answer “BLACK” or “RED”. If he says anything else you will ALL be executed immediately.

If he guesses the right color of the hat on his head he is set free, otherwise he is put to death. And we move on to the one in front of him and ask him the same question and so on…

Well, good luck tomorrow, HA HA HA HA HA HA!”

Now since you all can communicate freely during the night, can you find a way to guarantee the freedom of some prisoners tomorrow?
How many will win their freedom?

All of them
Back man will see 19 hats and so be able to call his own colour and go free.
Man 19 gets the call from behind plus the 18 he sees and so can work out his own.
Man 18 gets 2 calls plus the 17 right down the front man who has hear all 19 behind him call their colour so will be able to work out his own. .

 

[classic33]

All of them
Back man will see 19 hats and so be able to call his own colour and go free.
Man 19 gets the call from behind plus the 18 he sees and so can work out his own.
Man 18 gets 2 calls plus the 17 right down the front man who has hear all 19 behind him call their colour so will be able to work out his own. .

No

 

[Archie_tect]

If they organise a code for how they say their own colour they can give the person in front a code for whether their hat is black or red, eg the pitch of the voice or they could sing it for red or say it for black so the person in front will definitely know from the person behind whether his is black or red, so 19 will be guaranteed to be safe, only the person at the back has to guess and will have a 50% chance.

 

[nickyboy]

All of them
Back man will see 19 hats and so be able to call his own colour and go free.
Man 19 gets the call from behind plus the 18 he sees and so can work out his own.
Man 18 gets 2 calls plus the 17 right down the front man who has hear all 19 behind him call their colour so will be able to work out his own. .

The reason it's a "no" (and to give us some solidarity in our misery) is, I think, because there could be 20 red hats, or 20 black hats, or any combination thereof. So the prisoner can't look at the ones in front and determine his hat colour.....I think.

If you can explain my "no" I would appreciate it !

 

[Rasmus]

If you can explain my "no" I would appreciate it !

I suspect there is a way of getting a better outcome than 50% + some by chance, although I have not found it.

Of course, you could argue that the question did not stipulate the "best" method, only

can you find a way to guarantee the freedom of some prisoners tomorrow?

and your response should therefore be considered correct.

 

[benb]

Uneqal Marathon!
Alice and Bob run a standard 26.2-mile marathon race.
Bob's pace is a constant 8 minutes/mile, start to finish.
Alice's pace is such that for every 1-mile segment of the race, she takes 8:01 minutes.
That is, between mile markers 10 and 11, Alice consumes 8:01 minutes.
And between miles 6.374 and 7.374, Alice consumes 8:01 minutes.

Is Bob the sure winner of the marathon?

Well Bob finishes in 209.6 minutes (26.2 * 8)
Alice finishes 26 miles in 208.442 minutes, plus the final 0.2 miles in (481 seconds *0.2) = 96 seconds = 1.6 minutes, so 210.04 minutes

So Bob is the winner.

 

[classic33]

The reason it's a "no" (and to give us some solidarity in our misery) is, I think, because there could be 20 red hats, or 20 black hats, or any combination thereof. So the prisoner can't look at the ones in front and determine his hat colour.....I think.

If you can explain my "no" I would appreciate it !

Working from the answer given for the question
First guy is a coin toss - let's wish him good luck.
His job is to establish the parity of black hats visible to him.
He says "Black" if he sees an odd number of black hats; "Red" otherwise.
By paying attention to what has been said, each prisoner will know his hat's color.

Example:
Second to speak hears "Black" and sees an even number of black hats.
He knows his hat is black [odd changed to even - must be his is black] and says "black".

Third guy has heard "black" and "black" and sees an even number of black hats.
He knows his hat is red [even stayed even - his hat can't be black] and says "red".

And so on, to the front of the line.