Solve Enjoyable Enigmas with Mr.E's Challenge

  • Thread starter Thread starter Enigman
  • Start date Start date
AI Thread Summary
The forum thread invites puzzle enthusiasts to share various types of puzzles, including cryptograms and whodunnits, while emphasizing that participants should know the answers without resorting to online searches. A code message is presented, which participants attempt to decode, leading to discussions about its meaning and possible interpretations. Participants also engage in solving additional puzzles, such as cutting a cake into pieces with minimal cuts and a physics challenge involving water and matchsticks. The conversation highlights the enjoyment of problem-solving and the creative thinking required to tackle these enigmas. Overall, the thread fosters a collaborative atmosphere for sharing and solving intriguing puzzles.
  • #701
He climbed on a block of ice to tie the rope. It subsequently melted, leaving a water stain and a locked room mystery.
 
Physics news on Phys.org
  • #702
Ibix said:
He climbed on a block of ice to tie the rope. It subsequently melted, leaving a water stain and a locked room mystery.
This is correct. (It is the solution to the hanging man enigma.) :smile:
 
  • #703
Regarding the dalmations, I think collinsmark's solution is correct, but can be expressed rather more simply.

It is indeed a proof by contradiction. Imagine a set of eleven dogs from which we cannot pick a subset divisble by eleven. Line the dogs up in a row - sit! Stay! Let us say that the ith dog has Si spots.

In front of each dog, write the remainder when its spots plus the spots of all dogs to its left are divided by eleven. That is, in front of the ith dog, write the remainder when \sum_{k=1}^i S_k is divided by 11.

You now have eleven numbers. If any two of them are the same, then the intervening dogs' spots must add to a multiple of 11 (so if the nth and mth remainders are the same then \sum_{k=n+1}^m S_k is divisible by eleven.

So if no sets are divisible by eleven then you have eleven distinct non-zero remainders from division by eleven - but there are only ten such numbers. That is a contradiction - therefore you can always find a subset whose spots add to a multiple of eleven.
 
  • Like
Likes 1 person
  • #704
Ibix said:
Regarding the dalmations, I think collinsmark's solution is correct, but can be expressed rather more simply.

It is indeed a proof by contradiction. Imagine a set of eleven dogs from which we cannot pick a subset divisble by eleven. Line the dogs up in a row - sit! Stay! Let us say that the ith dog has Si spots.

In front of each dog, write the remainder when its spots plus the spots of all dogs to its left are divided by eleven. That is, in front of the ith dog, write the remainder when \sum_{k=1}^i S_k is divided by 11.

You now have eleven numbers. If any two of them are the same, then the intervening dogs' spots must add to a multiple of 11 (so if the nth and mth remainders are the same then \sum_{k=n+1}^m S_k is divisible by eleven.

So if no sets are divisible by eleven then you have eleven distinct non-zero remainders from division by eleven - but there are only ten such numbers. That is a contradiction - therefore you can always find a subset whose spots add to a multiple of eleven.
Yes. I like your solution in that it's far easier to conceptualize compared to mine, me thinks. :smile:
It does add some insight into what I was doing though. In your solution, the striving to keep any resulting number (in front of the dog) from being 0 or from being equal to any other dog's number, is equivalent to my solution's Fn number restrictions removing a unique, non-zero number as a valid choice (for each dog). After that, your solution and mine are pretty much identical in the fact that we run out of numbers before we run out of dogs.
 
  • #705
Next one-

A group of prisoners are trapped in a forcefield (like an invisible wall). These prisoners are perfectly brave, meaning that a prisoner would attempt an escape if he has any positive probability of success. The prisoners are monitored by a guard who has only one bullet in his gun, but who also has perfect marksmanship skills (he never misses).

The prisoners have overheard the guard saying "I have only one bullet left!". A maintenance technician needs to tune up the forcefield generator, and so for one second, the forcefield is released. How can the prisoners be kept detained?
 
  • #706
Taking "any positive probability of success" literally, the problem is that if all n > 1 prisoners dash out, the guard can only shoot one of them so they have a probability of (n - 1)/n of escaping. So I'm thinking that this is the "problem" you need to solve / prevent.

Is it something as simple as saying "I will shoot the first one to come out", after which they will all wait for another one to go first?
 
  • #707
Is it something as simple as saying "I will shoot the first one to come out", after which they will all wait for another one to go first?

Correct.

More clear might be "the first person to lift his leg will be shot."
 
  • #708
consciousness, if the guard does that then as a prisoner I
shove another prisoner, making him stumble and wasting the guard's bullet
 
  • #709
Or everyone agrees to go together...
1/n chance...
 
  • #710
Office_Shredder said:
consciousness, if the guard does that then as a prisoner I
shove another prisoner, making him stumble and wasting the guard's bullet

The best answer is perhaps then "the first one to make any movement in the next second will be shot!"

Enigman said:
Or everyone agrees to go together...
1/n chance...

There is bound to be a small time lag so technically they can't go together. It is assumed that the guard is very alert. He can detect this small lag and know who moved first. (In hindsight a programmable turret gun would have worked better)
 
  • #711
consciousness said:
It is assumed that the guard is very alert. He can detect this small lag and know who moved first. (In hindsight a programmable turret gun would have worked better)
So? The other prisoners still escape. The act of moving first is random and hence all of them as far they are concerned have 1 -1/n chance of survival.
 
  • #712
Enigman said:
So? The other prisoners still escape. The act of moving first is random and hence all of them as far they are concerned have 1 -1/n chance of survival.

I always made the assumption that the prisoners would wait for others to move and ensure their survival. But now I am convinced that your post destroys this solution!

So the correct answer hasn't been posted yet. An alternative solution that doesn't warrant assumptions about the behaviour of the prisoner exists.
 
  • #713
(The prisoners know that the other prisoners are perfectly brave.)
Hint-
You can assign numbers to make the prisoners distinguishable.
 
  • #714
Shoot the technician and wait until more bullets arrive. This is assuming the force field won't break down if the tune up gets delayed a little.
 
  • #715
Assuming it takes the prisoners more than one second to escape the guard's line of fire: Assign the prisoners numbers 1,...,n. Then the guard announces "When the shield goes back up I will kill the prisoner whose number is lowest that is not inside the shield.

1 can't try to escape or he will die. 2 knows this, so knows he can't try to escape either. Etc.
 
  • #716
Next one-
samuel_morse_poster-rcf54bcfac63b44ce81f6844619bc1859_wvc_8byvr_512.jpg


.-- --- .-- / -.-- --- ..- / -.-. .- -. / ... . . / -- .
Google search is allowed.
 
  • #717
Running out of ideas for Enigmas...:redface:
 
  • #718
Office_Shredder said:
Assuming it takes the prisoners more than one second to escape the guard's line of fire: Assign the prisoners numbers 1,...,n. Then the guard announces "When the shield goes back up I will kill the prisoner whose number is lowest that is not inside the shield.

1 can't try to escape or he will die. 2 knows this, so knows he can't try to escape either. Etc.

Correct!

Also shooting the tecnician might work but the prisoners will most probably not believe the guard.
 
  • #719
Enigman said:
Next one-
samuel_morse_poster-rcf54bcfac63b44ce81f6844619bc1859_wvc_8byvr_512.jpg


Samuel Morse. No need to search. Answer is in the URL of the picture.
 
  • #720
cArma said:
Samuel Morse. No need to search. Answer is in the URL of the picture.

Not the question ...
What does that post mean?
A bit 'under the belt' Enigma...
But since you quoted it, it should be easier...
 
  • #721
Wow I can see you!
 
  • #722
Office_Shredder said:
Assuming it takes the prisoners more than one second to escape the guard's line of fire: Assign the prisoners numbers 1,...,n. Then the guard announces "When the shield goes back up I will kill the prisoner whose number is lowest that is not inside the shield.

1 can't try to escape or he will die. 2 knows this, so knows he can't try to escape either. Etc.

Is this fundamentally different from what I said initially?
 
  • #723
consciousness said:
Wow I can see you!

Sold!
:approve:
 
  • #724
CompuChip said:
Is this fundamentally different from what I said initially?
There is a subtle difference.
If the prisoners decide to rush out together, a prisoner can unconsciously be the first to move. His demise is certain but the probability of his dying wasn't one when he made the decision!
Now in this solution if the prisoner numbered 1 decides to go first then he makes a conscious decision to kill himself! This starts the domino effect.
 
  • #725
The Enigma That Killed Homer.

I generally hate it when a movie or T.V. show 'adapts' some real world event to suit itself. But just sometimes these leave me grinning ear to ear, like the last Doctor who finale- It's prophesied that at some place (don't remember the name) a question will be asked to the Doctor and it is at this place he will die- obvious conclusion don't go to that place...well, Doctor didn't oblige and so didn't Homer (Iliad guy NOT yellow toon whose guts I hate).
It was foretold by The Oracle of Delphi that Homer would die in the island of Ios and that he should beware of a riddle posed to him by some young boys. Well obviously old Homer disregarded the prophecy and while he was walking on the banks of Ios a group of fisher boys asked him a riddle:

“What we caught, we threw away; what we didn’t catch, we kept. What did we keep?”

Unable to solve the riddle, Homer eventually died on the island, refusing to leave until he discovered the answer. So can you solve it?
(Googling is not allowed)
 
  • #726
Enigman said:
Next one-
samuel_morse_poster-rcf54bcfac63b44ce81f6844619bc1859_wvc_8byvr_512.jpg


.-- --- .-- / -.-- --- ..- / -.-. .- -. / ... . . / -- .
Google search is allowed.
what_hath_god_wrought.png

[Source: http://abstrusegoose.com/255]
 
  • #727
It itches...:frown:
 
  • #728
Enigman said:
It was foretold by The Oracle of Delphi that Homer would die in the island of Ios and that he should beware of a riddle posed to him by some young boys. Well obviously old Homer disregarded the prophecy and while he was walking on the banks of Ios a group of fisher boys asked him a riddle:

“What we caught, we threw away; what we didn’t catch, we kept. What did we keep?”

Unable to solve the riddle, Homer eventually died on the island, refusing to leave until he discovered the answer. So can you solve it?
(Googling is not allowed)


Is it bait?
 
  • #729
collinsmark said:
Is it bait?

Nope, what you couldn't catch you had to keep, unfortunately...
 
  • #730
Enigman said:

“What we caught, we threw away; what we didn’t catch, we kept. What did we keep?”


Hmm. How's about this guess:
"Mistakes." As in, if you catch your mistake in time, you can conceivably correct it (the mistake goes away), and all is good. But if you don't catch your mistake in time, you have to live with it.
 
  • #731
collinsmark said:
Hmm. How's about this guess:
"Mistakes." As in, if you catch your mistake in time, you can conceivably correct it (the mistake goes away), and all is good. But if you don't catch your mistake in time, you have to live with it.
Hmmm...*Scratches the E head* might work but not the answer the fishermen were talking about
Enigman said:
It itches...:frown:
 
  • #732
Lice!
 
  • #733
Haha!
 
  • #734
Okay, here's a new one. (And back to morbid.)

A man is recently dead, alone in an empty field. He died a quick and traumatic death. The man was young and healthy immediately before the time of his death. The only belongings the man had with him are the clothes on his back and an unopened package. The man would have survived had he opened the package.

So the question is, what is in the package?
 
  • #735
It is a little worrying how many of these puzzles involve dead guys.

A parachute
 
  • #736
Ibix said:
It is a little worrying how many of these puzzles involve dead guys.

A parachute
Yup.
 
  • #737
How quickly can you find out what is so unusual about this paragraph? It looks so ordinary that you would think that nothing is wrong with it at all, and, in fact, nothing is. But it is unusual. Why? If you look at it, study it and think about it, you may find out, but I am not going to assist you in any way. You must do it without coaching. No doubt, if you work at it for long, it will dawn on you. Who knows? Go to work and try your skill. Par is about half an hour. So jump to it and try your skill at figuring it out. Good luck --don't blow your cool.
 
  • #738
consciousness said:
How quickly can you find out what is so unusual about this paragraph? It looks so ordinary that you would think that nothing is wrong with it at all, and, in fact, nothing is. But it is unusual. Why? If you look at it, study it and think about it, you may find out, but I am not going to assist you in any way. You must do it without coaching. No doubt, if you work at it for long, it will dawn on you. Who knows? Go to work and try your skill. Par is about half an hour. So jump to it and try your skill at figuring it out. Good luck --don't blow your cool.
Hmm.

I think I know the solution. But I don't want to blurt it out so soon. I'll just say, as a hint, that if I am right, this post maintains this "unusual" condition.
 
  • #739
collinsmark said:
Hmm.

I think I know the solution. But I don't want to blurt it out so soon. I'll just say, as a hint, that if I am right, this post maintains this "unusual" condition.

Apart from the word "the"
 
  • #740
:smile: I see that you guys have figured it out!
 
Last edited:
  • #741
Jonathan Scott said:
Apart from the word "the"
Oooh. My bad.
 
  • #742
consciousness said:
How quickly can you find out what is so unusual about this paragraph? It looks so ordinary that you would think that nothing is wrong with it at all, and, in fact, nothing is. But it is unusual. Why? If you look at it, study it and think about it, you may find out, but I am not going to assist you in any way. You must do it without coaching. No doubt, if you work at it for long, it will dawn on you. Who knows? Go to work and try your skill. Par is about half an hour. So jump to it and try your skill at figuring it out. Good luck --don't blow your cool.

Okay, I'll blurt it out now before moving on.
The entire paragraph does not contain the letter 'e'. (My previous attempt at writing a reply which also did not contain the letter 'e' failed because I looked right over the word "the" that I used. Writing a coherent paragraph without a single 'e' is harder than I thought.)
 
  • #743
Back to morbid.

Two men are dead in a cabin, recently dying traumatic deaths. The cabin is in the wilderness. There are no roads to the cabin, nor nearby harbors that would allow one to reach the cabin by boat. There are no nearby runways or helicopter pads. There isn't even a footpath available to get to or from the cabin. There are no tunnels either. The two men were young and healthy immediately before their deaths. As a matter of fact, when they walked through the cabin door that morning, after having a nice breakfast and coffee, they felt bright and refreshed.

How did these men die?
 
  • #744
collinsmark said:
Back to morbid.

Two men are dead in a cabin, recently dying traumatic deaths. The cabin is in the wilderness. There are no roads to the cabin, nor nearby harbors that would allow one to reach the cabin by boat. There are no nearby runways or helicopter pads. There isn't even a footpath available to get to or from the cabin. There are no tunnels either. The two men were young and healthy immediately before their deaths. As a matter of fact, when they walked through the cabin door that morning, after having a nice breakfast and coffee, they felt bright and refreshed.

How did these men die?

They were beat to death by a wild pack of e's!

But seriously...traumatic deaths? Hmm.

Did they get picked up in the cabin by a tornado and dropped from a great height?
 
  • #745
cabin was in a ship and a storm hit?
 
  • #746
Enigman said:
cabin was in a ship and a storm hit?

Ooooo you're good :biggrin:
 
  • #747
lisab said:
They were beat to death by a wild pack of e's!

I resent that accusation...of incompetency obviously...when ##\mathcal E## strikes, no one traces it back to M##\mathcal E##, I am that good...
##\mathcal E##:-p
 
  • #748
lisab said:
They were beat to death by a wild pack of e's!

But seriously...traumatic deaths? Hmm.

Did they get picked up in the cabin by a tornado and dropped from a great height?

There are no tornadoes necessary for this one.

Enigman said:
cabin was in a ship and a storm hit?

Similarly, there are no storms necessary either. [Edit: nor did they arrive by sea. If you wish, there are no oceans or lakes anywhere near the cabin.]

There may or may not have been a storm/tornado involved, but it's not particularly relevant. All said though, the cabin is probably not in pristine condition (that's a hint).

For this riddle, I'll entertain any yes or no questions. But be warned, this riddle has high likelihood of producing seemingly contradictory answers to some yes or no questions, depending on the particular wording of the question.
 
Last edited:
  • #749
collinsmark said:
Back to morbid.

Two men are dead in a cabin, recently dying traumatic deaths. The cabin is in the wilderness. There are no roads to the cabin, nor nearby harbors that would allow one to reach the cabin by boat. There are no nearby runways or helicopter pads. There isn't even a footpath available to get to or from the cabin. There are no tunnels either. The two men were young and healthy immediately before their deaths. As a matter of fact, when they walked through the cabin door that morning, after having a nice breakfast and coffee, they felt bright and refreshed.

How did these men die?
...Attempt 2:
Cabin in an aircraft and it crashed?
 
  • Like
Likes 1 person
  • #750
Enigman said:
...Attempt 2:
Cabin in an aircraft and it crashed?

Yes, that's the correct answer. :smile:
They are in an airplane cabin. The airplane crashed.
 

Similar threads

Challenge Intermediate Math Challenge - August 2018
Replies
20
Views
6K
Challenge Are You Ready for the Basic Math Challenge This August?
2
Replies
57
Views
11K
Challenge Basic Math Challenge - September 2018
Replies
38
Views
8K
Challenge Intermediate Math Challenge - September 2018
Replies
28
Views
6K
Challenge Math Challenge - December 2018
2
Replies
67
Views
14K
Challenge Can You Solve These Math Challenges?
2
Replies
82
Views
15K
Codebreaker Wanted~Find the diamonds
Replies
15
Views
5K
Admissions Comments on PhD Statement of Purpose
Replies
6
Views
2K
Challenge Intermediate Math Challenge - May 2018
2
Replies
61
Views
12K
Challenge Intermediate Math Challenge - July 2018
Replies
16
Views
6K

Hot Threads

Recent Insights

Back
Top