ASF Puzzles & Conundrums Thread

craft · 5 May 2015

bellenuit said:
BTW, this is referred to as Einstein's Riddle and I read about it here. I would be surprised if only 2% of the population can solve it as I didn't think it very difficult. It involved a lot of steps, but the logic was fairly straightforward.

Einstein's Election Riddle: are you in the two per cent that can solve it?

http://www.theguardian.com/science/...are-you-in-the-two-per-cent-that-can-solve-it

I always knew the Einstein puzzle as a challenge to assumptions. But it was worded slightly differently. “Who keeps fish”?

In that case the answer is - You can’t know.

You can know who doesn’t keep fish but you can’t know that (Nigel in this scenario) keeps fish – he could have any pet other then the four mentioned.

By wording it who owns the fish implies there is a fish and changes it to a straight logic test rather than a challenge to assumptions – perhaps the 2% related to the original wording of the riddle and refers to the % who challenge assumption rather than the % who can do logic puzzles. Who knows the basis or robustness of the 2% claim?

craft · 5 May 2015

Tisme said:
I remember my pursuit of lateral thinking started in earnest when my grade six teacher posed this question:

A man form Kenya, with black hair and black gloves, otherwise dressed completely in black, wearing a black ski mask, stands at an intersection looking north in a totally black-painted town that is facing west. All of the street lamps in town are broken. There is no moon. A matt black car heading south, with no reflectors nor lamps drives straight toward him, but swerves in time to miss him. How did the driver know to swerve?

This one also seems to be questioning assumptions as there is nothing to stop it being full sun middle of the day.

galumay · 5 May 2015

craft said:
This one also seems to be questioning assumptions as there is nothing to stop it being full sun middle of the day.

That was the conclusion I came to, - that it was daytime.

skc · 5 May 2015

Tisme said:
I remember my pursuit of lateral thinking started in earnest when my grade six teacher posed this question:

A man form Kenya, with black hair and black gloves, otherwise dressed completely in black, wearing a black ski mask, stands at an intersection looking north in a totally black-painted town that is facing west. All of the street lamps in town are broken. There is no moon. A matt black car heading south, with no reflectors nor lamps drives straight toward him, but swerves in time to miss him. How did the driver know to swerve?

Lol. A great question for when we were kids. These days, children will probably say things like "automatic avoidance system" was activated.

galumay · 5 May 2015

skc said:
Lol. A great question for when we were kids. These days, children will probably say things like "automatic avoidance system" was activated.

I am pleased to say my 11 year old worked it out!

Craton · 5 May 2015

galumay said:
That was the conclusion I came to, - that it was daytime.

At the risk of being labelled, my way of thinking was in the whites of the eyes.

bellenuit · 11 May 2015

This is a subset of a puzzle that has proved controversial over the years.

A king has dominion over several islands each filled with slaves. The slaves have either blue or brown eyes. Some islands have just blue eyed slaves, some have just brown eyed slaves and some have a mixture of both.

The slaves on these islands are very smart and logical. Each has a burning ambition to be made free and travel to the mainland where the king and all the free people live.

The only way the slaves can become free is by deducing the colour of their own eyes and having done so they must depart the island that very day for the mainland on one of the many boats that go back and forth each day. This is not so easy as although the slaves can see the colour of everybody else's eyes, there are no reflective surfaces that allow them to see the colour of their own eyes. Additionally, slaves are never allowed discuss other slaves' eye colours so cannot tell or indicate in any way to another slave what eye colour that other slave has.

On one island there are just 3 slaves, all with blue eyes. One Monday morning, a king's official is visiting the island to check on things. Later that morning, as he is about to get on one of the many ferries back to the mainland, he is asked by the captain: "Does everyone on this island have brown eyes?". He answers: "No". Both the question and the response are overheard by the 3 slaves.

The question is, what (apart from the normal mundane daily drudgery of slaves) happens that week on the island once the slaves hear this seemingly redundant information?

cynic · 11 May 2015

I'll take a stab at it.

All three slaves individually arrive at the erroneous conclusion that they are the only slave on the island with brown eyes.

Upon observing that all three have boarded the next ferry off the island, all three slaves then realise their unanimous error, and now know that they must all have blue eyes.

skc · 11 May 2015

bellenuit said:
This is a subset of a puzzle that has proved controversial over the years.

A king has dominion over several islands each filled with slaves. The slaves have either blue or brown eyes. Some islands have just blue eyed slaves, some have just brown eyed slaves and some have a mixture of both.

The slaves on these islands are very smart and logical. Each has a burning ambition to be made free and travel to the mainland where the king and all the free people live.

The only way the slaves can become free is by deducing the colour of their own eyes and having done so they must depart the island that very day for the mainland on one of the many boats that go back and forth each day. This is not so easy as although the slaves can see the colour of everybody else's eyes, there are no reflective surfaces that allow them to see the colour of their own eyes. Additionally, slaves are never allowed discuss other slaves' eye colours so cannot tell or indicate in any way to another slave what eye colour that other slave has.

On one island there are just 3 slaves, all with blue eyes. One Monday morning, a king's official is visiting the island to check on things. Later that morning, as he is about to get on one of the many ferries back to the mainland, he is asked by the captain: "Does everyone on this island have brown eyes?". He answers: "No". Both the question and the response are overheard by the 3 slaves.

The question is, what (apart from the normal mundane daily drudgery of slaves) happens that week on the island once the slaves hear this seemingly redundant information?

There is no mention of what happens when you guess wrong? Given that it's a 50/50 guess... a slave should simply guess blue on day 1 and brown on day 2. It's a wonder that there are any slaves left at all.

bellenuit · 11 May 2015

skc said:
There is no mention of what happens when you guess wrong?

I didn't think I needed to be explicit about that as the text clearly said "the only way the slaves can become free is by deducing the colour of their own eyes".

Deducing and guessing are not the same.

I will add the following clarification to prevent guessing.

Slaves must at all times strive to logically determine what their eye colour is based on everything they know and having made the determination that they know without doubt what their eye colour is must leave for the mainland that same day otherwise they will be put to death as it is not allowed to remain on the island if you know your eye colour. If a slave boards the ferry to leave, he must explain to the captain his reasoning for assuming he now knows his eye colour. If the logic is incorrect or if the slave simply made a guess and cannot demonstrate any logic to his determination, then the slave will immediately be put to death.

cynic · 11 May 2015

On further consideration. The slaves realise that the ferry captain was colour blind and seeing blue as brown. The slaves now know that they are all blue eyed.

trainspotter · 11 May 2015

bellenuit said:
On one island there are just 3 slaves, all with blue eyes. One Monday morning, a king's official is visiting the island to check on things. Later that morning, as he is about to get on one of the many ferries back to the mainland, he is asked by the captain: "Does everyone on this island have brown eyes?". He answers: "No". Both the question and the response are overheard by the 3 slaves.

The question is, what (apart from the normal mundane daily drudgery of slaves) happens that week on the island once the slaves hear this seemingly redundant information?

On the 3rd day they all leave as they have deduced that they all have blue eyes. Once the kings official announces that the islanders have blue eyes and confirming with the captain it becomes common knowledge. The first slave can see that the other 2 have blue eyes. The second slave can see that the other 2 have blue eyes. The third slave can see the other 2 have blue eyes. Then Robinson Crusoe gets all the work done by Friday

bellenuit · 11 May 2015

trainspotter said:
Once the kings official announces that the islanders have blue eyes and confirming with the captain it becomes common knowledge. The first slave can see that the other 2 have blue eyes. The second slave can see that the other 2 have blue eyes. The third slave can see the other 2 have blue eyes. Then Robinson Crusoe gets all the work done by Friday

I don't see your logic. The official didn't say that everyone has blue eyes. He said NO to the question: "Does everyone have brown eyes". Wasn't that already common knowledge before the official arrived?

trainspotter · 11 May 2015

bellenuit said:
I don't see your logic. The official didn't say that everyone has blue eyes. He said NO to the question: "Does everyone have brown eyes". Wasn't that already common knowledge before the official arrived?

Nope because the slaves are not allowed to talk to each other about their eye colour. By the official stating the question and the captain answering in the affirmative that they do not ALL have brown eyes. There is the possibility that the slaves think that one of them has brown eyes but by the third day they would have deduced they all have blue eyes because one slave can see the other 2 have blue eyes. The second slave can see the other 2 have blue eyes. The third slave can see the other 2 have blue eyes so with CERTAINTY they can say that they ALL have blue eyes. Follow my logic?

bellenuit · 11 May 2015

trainspotter said:
Nope because the slaves are not allowed to talk to each other about their eye colour. By the official stating the question and the captain answering in the affirmative that they do not ALL have brown eyes. There is the possibility that the slaves think that one of them has brown eyes but by the third day they would have deduced they all have blue eyes because one slave can see the other 2 have blue eyes. The second slave can see the other 2 have blue eyes. The third slave can see the other 2 have blue eyes so with CERTAINTY they can say that they ALL have blue eyes. Follow my logic?

Nope, I don't follow your logic. Before the official arrived, each slave could see that the other two had blue eyes. They also knew that all 3 of them didn't have brown eyes because they could see two others with blue eyes. So why did they on hearing the official state what they already knew make them all leave on the Wednesday?

I get the feeling you have come across the problem before, but have forgotten the deductive steps that they follow to arrive at knowing their own eye colour. Look at it from the perspective of the slave arriving at the boat and explaining to the captain why he now knows he has blue eyes. As far as I can see from your statement, the slave gives this as a reason:

It is the 3rd day and I know all 3 of us do not have brown eyes. I can see the other two have blue eyes, therefore I have blue eyes.

I fail to see why the captain would accept this as a logically deduced conclusion and not kill him.

You are on the right track, but I don't agree that you have given sufficient grounds for them leaving on the Wednesday.

Tisme · 11 May 2015

I'm guessing the prospect of freedom would drive them to kill the other two in hope they both have brown eyes?

bellenuit · 11 May 2015

Tisme said:
I'm guessing the prospect of freedom would drive them to kill the other two in hope they both have brown eyes?

? But each slave can see that the other two have blue eyes.

Tisme · 11 May 2015

bellenuit said:
? But each slave can see that the other two have blue eyes.

Mere details And you just found the answer then

bellenuit · 11 May 2015

Tisme said:
Mere details And you just found the answer then

I have no idea what you mean.

cynic · 12 May 2015

I think i've finally gotten it!

Each slave realises that if they have brown eyes then the other two slaves will see one blue eyed and one brown eyed slave. Each slave further realises that if one were to see two brown eyed slaves then that slave would know his/her eye colour must be blue and would leave the island that day. On the Tuesday when the slaves find that nobody left , they all recognise that this can only mean that at most there can only be one brown eyed slave.

However, on Wednesday morning when all slaves are still present, they are then able to deduce that there are no brown eyed slaves and safely depart the island.

P.S. I think this might be similar to T.S. answer.

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