Puzzle Corner

[gll99]

The answer to the houses and utilities:
Of course in the standard puzzle, it normally can't be done, so cheat or should I say, innovate. There is a loophole in the written rules. I learned this variation of the puzzle many years ago during problem solving exercises at a management seminar. They taught us not to create boundaries for ourselves that do not exist. That's why the boxes were deliberately drawn around the utilities creating an artificial boundary which the brain perceives as "do not cross", yet nothing in the rules prevents it.



edited:
btw) my lines are not drawn properly. They should all be touching the utility names and the cheat loop goes between the y and the d in hydro.

[daamon]

They taught us not to create boundaries for ourselves that do not exist. That's why the boxes were deliberately drawn around the utilities creating an artificial boundary which the brain perceives as "do not cross", yet nothing in the rules prevents it.

Ah yes, I guess we all assumed that we couldn't go through the suppliers, like we couldn't take the supply through the houses - I certainly did! Same moral as the "9 dots, 4 lines" one... Very good!

Similar to the door one asked earlier.

I land on a large island and want to reach the only town on the other side of the island. I come to a fork in the road but no markings indicate which way leads to town. I see a native standing there at the fork. I know that only 2 types of natives live on this island. Those who always lie and those who always tell the truth. I don't know to which group this native belongs. How do I find out which path will get me to town. The other way will lead deep into the jungle and night is approaching.

OK, here goes with my solution. I've numbered parts of the question so I can explain the solution:

You ask the native: If I were to ask you if this path (signal to one of the 2 paths (1)) would take me to town, and I took a path based on your response (2), would I get to town (3)?

It's only one question, albeit cleverly worded (I hope!), aimed at one native and gets the desired result. I can't see that I've flouted any rules...

Given that there are 2 paths and 2 types of native, there are 4 possible combinations of "which path" aimed at either native. These are covered in Cases A - D:

Case A) Identified path (1): Right one. Truthful native, so native's response (2) would've been "Yes", so actual response (3) would be "Yes".

Case B) Identified path (1): Right one. Lying native, so native's response (2) would've been "No", so actual response (3) would be "Yes".

Case C) Identified path (1): Wrong one. Truthful native, so native's response (2) would've been "No", so actual response (3) would be "No".

Case D) Identified path (1): Wrong one. Lying native, so native's response (2) would've been "Yes", so actual response (3) would be "No".

So this question identifies the path to town with a "Yes" response, and the path to the jungle with a "No" response, irrespective of whether the native lies or not.

How's that!?!?

[gll99]

daamon:

BINGO!!!!! We have a winner. The way I would word the question is "If I were to ask you if this road leads to town would you answer yes" and your similar question will as you surmised guarantee you the right answer no matter if the native is a truth teller or a liar. The wrong road will always get you a no answer and the right road will get you a yes. You can't miss with just one question.

Congratulations on solving a tricky one.
============================
The house a services puzzle fooled the whole group the day it was introduced to me. On day one of the course they showed us a standard version of the puzzle with 6 dots representing things to join with no reference to houses and services and after 10 or 15 minutes when no one could solve it they told us it was impossible. A few days into the course during problem solving exercises they pulled the one I posted on us. We all got fooled thinking this too couldn't be done because of the similarity. After much coaching someone finally found the loophole but by then we had been given many hints about not limiting our thinking and being stopped by perceived obstacles.
====================================
Speaking of perceptions,
The truck driver:
One day in an unfamiliar town, I happened to be following behind a Coca Cola truck driver as we slowly worked our way up a hill. I hadn't noticed that we were on a one way street but as we got near a corner I saw that we were going against the one way arrow. There was a cop parked on the side of the road and as we got near to him the cop yelled "hi Bill" to the truck driver as they waved to each other and he didn't stop him. I wasn't so lucky he stopped me and gave me a ticket for driving the wrong way on a one way street. I decided to fight the ticket claiming that the cop unfairly picked on me because I was a stranger and let his buddy get away. The judge, turned out to be the brother of the truck driver and he just laughed at me and the whole court room burst out in laughter too. I was so embarrassed. My conclusion is that the whole town must have been related. I'm not going back there again.

Do you think I was treated fairly or was this just a taste of good old small town dis-hospitality?

[Tommyknocker]

You were punished for breaking the law. Bill got away due to nepotism. If it were me, I would not have even fought the ticket, because I was guilty as sin. Regardless of what favoritism the truck driver received.

It reminds me of a joke I heard once. It seems a speeder was pulled over by the local constabulary. The perpetrator asked the cop why did he stop him and not all the other speeders. The cop asked him, "Do you fish?"
The speeder said "Yes, I fish."
The cop then asked, "When you do, do you catch all the fish?"

[gll99]

I appreciate what you said Tommyknocker. Does anyone else have a different take on the truck driver incident?

[daamon]

BINGO!!!!! We have a winner. Congratulations on solving a tricky one.

You're not kidding it was tricky - that's been bugging me for ages.

P.S. I'll now refrain from "hunting you down"...

@ gll99 - "The Truck Driver"

I'd say, according to the law (as in written, not the boys in uniform) you were treated fairly. Ignorance is not a defence (i.e. not knowing you were going the wrong way down a one-way street). If you claimed that this was because you were following a large vehicle, then you were too close.

That said, in your defence, you can quote the incident with the cop and Bill (the truck driver) but, as Tommyknocker pointed out, you're then up against small-town nepotism.

Of course, you could always take it higher - on principal - as I'd say that the whole legal system in that town could be corrupt and should at least be investigated.

Others would argue that a large vehicle going up a hill would be moving too slowly to present a danger to oncoming traffic and so the cop let it go using his common sense.

Interesting question...

[gll99]

daamon, Tommyknocker and others:

Since you have responded, I must admit to you that the "Truck Driver" scenario contains a puzzle of sorts. It is so well known that I invented a convoluted story to disguise it.

Given this information can you solve it?

Why did everyone laugh at me when I said the truck driver should have been charged. Was it really small town mentality, was the policeman biased, was the judge guilty of nepotism or is there something else I didn't reveal that's not quite right?

daamon:
After you read this the hunt may be back on. But I have moved from the island and am now in a small town following a Coca Cola truck driver

[northcat_8]

daamon, Tommyknocker and others:

Since you have responded, I must admit to you that the "Truck Driver" scenario contains a puzzle of sorts. It is so well known that I invented a convoluted story to disguise it.

Given this information can you solve it?

Why did everyone laugh at me when I said the truck driver should have been charged. Was it really small town mentality, was the policeman biased, was the judge guilty of nepotism or is there something else I didn't reveal that's not quite right?

daamon:
After you read this the hunt may be back on. But I have moved from the island and am now in a small town following a Coca Cola truck driver

I thought I had heard that story as a puzzle before.

[flaninacupboard]

you never stipulated the guy was in a truck, merely a truck driver.

[gll99]

flaninacupboard
Good stuff! You got it

I thought that once I exposed a bit of detail someone would catch the trick.

The original story simply says that a cop sees a truck driver heading the wrong way on a one way street and does nothing about it. Why not?

Since this was too easy I made it a little less obvious but I guess the clues were just too good.

[flaninacupboard]

it's not obvious, but after you said something is not right i picked it up straight away. i think it was the coca cola thing that did - it was extraneous information, a red herring. it's like in tv and films, when a character sees/gets told something totally random or irrelevant, you know it will become crucial to the plot in act III. i think soaps and sitcoms are worst for that.

[daamon]

daamon:
After you read this the hunt may be back on. But I have moved from the island and am now in a small town following a Coca Cola truck driver

Too right - and I've got a slight edge on you coz now I know (once again aided by my trusty countryman, flaninacupboard) that you're NOT in a Coca Cola truck...!

Yet another illustration of how we make assumptions rather than looking at the facts... You humble us Oh Great Renegade Wolf...

[daamon]

Is anyone (still) working on the "9 dots, 10 lines" one? northcat_8 has PM'd me the right answer, but I'd thought I'd ask before I post the solution...

[daamon]

The gold bracelet

A young man needs a place to stay for a week but only gets paid at the end of the week. The old lady landlord wants to be paid by the day and won't wait a week. She's had problems with people running out on her before and won't get caught again. The only thing of value that the young man has is a gold bracelet made up of seven loops linked together in a chain with a small clasp to close the bracelet. He could give her that and then buy it back at the end of the week. The bracelet is worth the value of the room for a week and the young man not trusting her either does not want to pay ahead and the lady won't accept less than one day's rent. She says she will accept one link of the bracelet each day as payment but she is concerned that the bracelet will lose value if damaged and adds one stipulation, the young man can only break the bracelet once. How can he not underpay or overpay on a daily basis with just one separation ?

The young man breaks the third link, leaving him with two connected links, one open (broken) link, and the four remaining connected links.

Day 1: Pay with the 1 open link.
Day 2: Hand over the 2 joined links, and get the 1 open link back.
Day 3: Hand over the 1 open link.
Day 4: Hand over the joined 4 links and get the 2 joined links and 1 open link back.
Day 5: Hand over the 1 open link.
Day 6: Hand over the 2 joined links, and get the 1 open link back.
Day 7: Either hand over the 1 remaining (open) link (if he's not been paid), or pay cash and get all the 6 links back that the old lady has.

How's that!?!?

[gll99]

daamon wrote

The young man breaks the third link, leaving him with two connected links, one open (broken) link, and the four remaining connected links.

Day 1: Pay with the 1 open link.
Day 2: Hand over the 2 joined links, and get the 1 open link back.
Day 3: Hand over the 1 open link.
Day 4: Hand over the joined 4 links and get the 2 joined links and 1 open link back.
Day 5: Hand over the 1 open link.
Day 6: Hand over the 2 joined links, and get the 1 open link back.
Day 7: Either hand over the 1 remaining (open) link (if he's not been paid), or pay cash and get all the 6 links back that the old lady has.

How's that!?!?

You got it! that's how it's done. I had to write it down from memory so I don't know if I gave away too much info in describing the puzzle.
I own a book (now misplaced) that has many pages of puzzles like that but can't find it right now. One has to do with pulling socks out of a drawer in the dark to get a matching pair. Another has to do with black and white marbles in a box, geometry type puzzles etc.... Unfortunately the old brain cells have not kicked in yet so I will have to wait until I find my book again. I only have to look through a hundred or so boxes and containers in the basement storage. You know what they say it's always in the last place you look that you find what your looking for. (what idiot finds it and then keeps looking )

[daamon]

One has to do with pulling socks out of a drawer in the dark to get a matching pair.

"Socks In A Drawer":

It's pitch black and there are 12 individual socks in a drawer, not paired up with a matching sock - they're all singles socks messed up in a random arrangement. 6 of the socks are blue and 6 are black - How many socks do you need to take out to get a matching pair?

EDIT: Thanks to northcat_8 for pointing out the glaring omission... (I missed out the word "matching" - was tempted to leave it out and see how many people gave a number greater than 2!)

You know what they say it's always in the last place you look that you find what your looking for. (what idiot finds it and then keeps looking )

[SquirrelDip]

@daamon: Part II of the glaring omission, how many do you need to pull out to get a GUARANTEE matching pair. Without the guarantee the answer is 2 with a 5/11 probability...

[daamon]

@daamon: Part II of the glaring omission, how many do you need to pull out to get a GUARANTEE matching pair. Without the guarantee the answer is 2 with a 5/11 probability...

Nope, I disagree - you don't need the word "guaranteed". There is a minimum number of socks (max. 12, of course) that you can take out that WILL get you a matching pair.

[SquirrelDip]

@daamon: Part II of the glaring omission, how many do you need to pull out to get a GUARANTEE matching pair. Without the guarantee the answer is 2 with a 5/11 probability...

Nope, I disagree - you don't need the word "guaranteed". There is a minimum number of socks (max. 12, of course) that you can take out that WILL get you a matching pair.

The maximum number of socks that you need to pull out to guarantee a matching pair is 3.

Without the "guarantee" you have, almost, a 50/50 chance of getting a matched pair with 2 socks.

[daamon]

Yep.

Not wanting to steal gll99's thunder - I guess that's the one you were referring to?

[SquirrelDip]

Here's something along the same line:

Take a single, simple, six sided die. How many rolls must you make to guarantee get a 6?

[daamon]

"Getting a 6 on a die"

I would say the answer is "infinity". Here's my reasoning:

Statistically, you've a 1 in 6 chance of getting any number on a single roll of the die. So, the chance of getting a 6, per roll, is 1/6.

As the rolling of a die is an independent event from any previous roll of the die (i.e. the outcome of the previous roll doesn't have a bearing on the next roll), the probability of getting a 6 on each and every successive roll is still 1 in 6 - irrespective of how many times you roll the die.

Therefore, statistically, you'd expect to get a 6 if you were to roll the die 6 times, but it's not guaranteed (as you stipulated). In fact, you're as likely to get no 6's as you are six 6's (as hard as it is to believe) with 6 rolls of the die. In fact, taking it further, the same applies for a million rolls of the die - the chance of no 6's is the same as the chance of a million 6's. This is because you're rolling on die a million times, not a million dice one time all together.

So, you could roll the die an inifinite number of times and not get a 6, and so having to roll X number of times again until you get a six. But, infinity + X = infinity, hence my answer.

I've haven't used my probability, perms and coms maths for a while so there may be a flaw. But I think my logic is sound.

northcat_8 - You seem clued up on this kinda stuff, what d'ya reckon?

[SquirrelDip]

@daamon: Correct!

Guarantee a 6 would take an infinite number of rolls, any other level of confidence would yield a finite number.

A 50% confidence would take 4 rolls, a 95% confidence would take 17 rolls.

1 Roll = (1/6)
2 Rolls = (1/6) + (5/6)*(1/6)
3 Rolls = (1/6) + (5/6)*(1/6) + (5/6)*(5/6)*(1/6)
etc...

(If I recall my basic probability correctly...)

[daamon]

The answer to "9 dots, 10 lines" (as reached by northcat_8):

[daamon]

New Puzzle: "Make A Square"

Make only 2 straight line cuts in the following shape to then be able to make a square.

Identify the lines using the letters around the shape.

[SquirrelDip]

How's this:

[daamon]

Spot on! I'm more impressed with your diagrams though - you'd make an excellent technical draftsman (if you're not already).

Another option is to cut along the lines D - K and M - H. Giving different shapes, but can still be re-arranged to form a square.

New Puzzle: "12 Numbers, 12 Squares"

The task is to place the 12 numbers (1 thru 12 inclusive) in to the 12 squares in the diagram below, such that no two squares that touch (even at corners) have consecutive numbers. There may be more than one correct solution.

[SquirrelDip]

@daamon: Here's 4:



Technical Draftsman... Bite your tongue! Pay cut would be hard to take but the reduction in responsibility would be refreshing...

(I don't know if you would consider this cheating but I wrote a program over my lunch break to solve the puzzle...)

[Capmaster]

Not in your guys league Daamon and Squirrel Dip, but here goes:

A man has two modern U.S. coins that total 30 cents. One of them is not a nickle. What are the coins?
(If you know the answer, please hold off or PM me - I want to see of Daamon or Squirrel Dip know)

[SquirrelDip]

@Capmaster: Used to love that one when I was a kid - I know the answer but will leave it to daamon...

P.S. Love the avatar - chuckle every time I see it...