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Chopzx

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Logical puzzles: work that brain Reply to this Post
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Do you enjoy logical puzzles which fry your brain?
No?
Didn't think so... But to those who do, I am posting in Emerald Events today to introduce you to Logical Events Part II. Thank you to Crazydonkey and llyarri for running the one before this one, however I am bored these days and I have had enough of re runs of TV shows, and I enjoy the thrill of people's amazing pirate-y faces when they receive a prize!

I will be posting one difficult puzzle and easy puzzle every Wednesday at some point during the day, but if I forget, don't be afraid to bump the thread or send me a /tell.

Prizes would be in random boxes ranging from trinkets to ship deeds and a pet if I have a few lying around. The prize would be awarded to the first person to send me the correct answer in a PM, or a tell, and those who come second and onwards would of course, get an honourable mention.

The winner and answer will be announced on the Tuesday at some point of the day.

Rules

#1 Only one entry each! If you found out you made a mistake, better luck next time.
#2 Do not, I repeat, NOT! post the answers in this thread. The event is supposed to be fun for all, don't ruin it for the persons that did not solve it yet.
#3 Put your pirate name on the Emerald ocean in the same PM as your answer.
#4 I only accept answers through PMs or tells.

Breaking rule #1 or #2 will result in Disqualification.

Feel free to send tells or PMs with questions regarding the thread or puzzle.

Good luck! I will post the first puzzle momentarily.
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Chopzx/Chopzx-East on Emerald
Chopzx/Chopzx-West on Meridian
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[Edit 1 times, last edit by Chopzx at Jun 17, 2013 11:42:34 PM]
[Jun 17, 2013 2:26:24 PM] Show Printable Version of Post        Send Private Message [Link]  Go to top 
Chopzx

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Re: Logical puzzles: work that brain Reply to this Post
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You are the king of The Cursed Isles and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You've got 1000 barrels of rum which you were planning to open for the celebration, but you find out that one of them is poisoned.

The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison.

You have over a thousand skellies and zombies at your disposal and just under 24 hours to determine which single bottle is poisoned.

You have a handful of prisoners... i mean pirates... about to be executed, and it would mar your celebration to have anyone else killed.

What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?
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Chopzx/Chopzx-East on Emerald
Chopzx/Chopzx-West on Meridian
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[Edit 1 times, last edit by Chopzx at Jun 17, 2013 2:33:47 PM]
[Jun 17, 2013 2:33:04 PM] Show Printable Version of Post        Send Private Message [Link]  Go to top 
Chopzx

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Re: Logical puzzles: work that brain Reply to this Post
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Because the puzzle above is very difficult, here is an easier one.

Three men in a cafe order a meal the total cost of which is $15. They each contribute $5. The waiter takes the money to the chef who recognizes the three as friends and asks the waiter to return $5 to the men.

The waiter is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the $5 between the three he simply gives them $1 each and pockets the remaining $2 for himself.

Now, each of the men effectively paid $4, the total paid is therefore $12. Add the $2 in the waiters pocket and this comes to $14.....where has the other $1 gone from the original $15?
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Chopzx/Chopzx-East on Emerald
Chopzx/Chopzx-West on Meridian
[Jun 17, 2013 2:38:49 PM] Show Printable Version of Post        Send Private Message [Link]  Go to top 
Twittly

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Re: Logical puzzles: work that brain Reply to this Post
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Dat was fun!
----------------------------------------
~Twittly~ on "Sage" "Emerald" Ocean
Avatar by Yumisa!
Check out my gallery of other avatars
[Jun 17, 2013 5:36:47 PM] Show Printable Version of Post        Send Private Message [Link]  Go to top 
Chopzx

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Re: Logical puzzles: work that brain Reply to this Post
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Some very interesting answers to both the hard and easy logical puzzle however the winner and answers will be revealed this Friday at some point during the day.

Due to the fact that today is Wednesday, two more puzzles will be put up; One hard and one easy. Here is the first easy puzzle:

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different.

How do you measure 45 minutes?
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Chopzx/Chopzx-East on Emerald
Chopzx/Chopzx-West on Meridian
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[Edit 1 times, last edit by Chopzx at Jun 18, 2013 5:36:04 PM]
[Jun 18, 2013 5:34:02 PM] Show Printable Version of Post        Send Private Message [Link]  Go to top 
Chopzx

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Re: Logical puzzles: work that brain Reply to this Post
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Ten pirates land on Hinga island. There they find lots of coconuts and a monkey. During their first day they gather coconuts and put them all in a community pile. After working all day they decide to sleep and divide them into ten equal piles the next morning.

That night one castaway wakes up hungry and decides to take his share early. After dividing up the coconuts he finds he is one coconut short of ten equal piles. He also notices the monkey holding one more coconut. So he tries to take the monkey's coconut to have a total evenly divisible by 10. However when he tries to take it the monkey conks him on the head with it and kills him.

Later another castaway wakes up hungry and decides to take his share early. On the way to the coconuts he finds the body of the first castaway, which pleases him because he will now be entitled to 1/9 of the total pile. After dividing them up into nine piles he is again one coconut short and tries to take the monkey's slightly bloodied coconut. The monkey conks the second man on the head and kills him.

One by one each of the remaining castaways goes through the same process, until the 10th person to wake up gets the entire pile for himself.

What is the smallest number of possible coconuts in the pile, not counting the monkeys?
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Chopzx/Chopzx-East on Emerald
Chopzx/Chopzx-West on Meridian
[Jun 18, 2013 5:38:31 PM] Show Printable Version of Post        Send Private Message [Link]  Go to top 
Chopzx

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Re: Logical puzzles: work that brain Reply to this Post
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Sorry about this, but I am away looking at Universities, and I will post the winners and correct answers to the first two puzzles when I can
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Chopzx/Chopzx-East on Emerald
Chopzx/Chopzx-West on Meridian
[Jun 21, 2013 8:36:20 AM] Show Printable Version of Post        Send Private Message [Link]  Go to top 
Reddress



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Re: Logical puzzles: work that brain Reply to this Post
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by the way, please post the answers in a way so you don't read them if don't want to.
[Jun 21, 2013 8:41:56 AM] Show Printable Version of Post        Send Private Message [Link]  Go to top 
Chopzx

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Re: Logical puzzles: work that brain Reply to this Post
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You are the king of The Cursed Isles and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You've got 1000 barrels of rum which you were planning to open for the celebration, but you find out that one of them is poisoned.

The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison.

You have over a thousand skellies and zombies at your disposal and just under 24 hours to determine which single bottle is poisoned.

You have a handful of prisoners... i mean pirates... about to be executed, and it would mar your celebration to have anyone else killed.

What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?



Solution: 10 prisoners must sample the wine. Bonus points if you worked out a way to ensure than no more than 8 prisoners die.

Number all bottles using binary digits. Assign each prisoner to one of the binary flags. Prisoners must take a sip from each bottle where their binary flag is set.


With ten people there are 1024 unique combinations so you could test up to 1024 bottles of wine.

Each of the ten prisoners will take a small sip from about 500 bottles. Each sip should take no longer than 15 seconds and should be a very small amount. Small sips not only leave more wine for guests. Small sips also avoid death by alcohol poisoning. As long as each prisoner is administered about a millilitre from each bottle, they will only consume the equivalent of about one bottle of wine each.

Each prisoner will have at least a fifty percent chance of living. There is only one binary combination where all prisoners must sip from the wine. If there are ten prisoners then there are ten more combinations where all but one prisoner must sip from the wine. By avoiding these two types of combinations you can ensure no more than 8 prisoners die.

Loathe be the winner of this one. Next answer coming up
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Chopzx/Chopzx-East on Emerald
Chopzx/Chopzx-West on Meridian
----------------------------------------
[Edit 2 times, last edit by Chopzx at Jun 21, 2013 3:39:01 PM]
[Jun 21, 2013 3:35:33 PM] Show Printable Version of Post        Send Private Message [Link]  Go to top 
Chopzx

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Re: Logical puzzles: work that brain Reply to this Post
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Because the puzzle above is very difficult, here is an easier one.

Three men in a cafe order a meal the total cost of which is $15. They each contribute $5. The waiter takes the money to the chef who recognizes the three as friends and asks the waiter to return $5 to the men.

The waiter is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the $5 between the three he simply gives them $1 each and pockets the remaining $2 for himself.

Now, each of the men effectively paid $4, the total paid is therefore $12. Add the $2 in the waiters pocket and this comes to $14.....where has the other $1 gone from the original $15?


Solution: The payments should equal the receipts. It does not make sense to add what was paid by the men ($12) to what was received from that payment by the waiter ($2)

Although the initial bill was $15 dollars, one of the five dollar notes gets changed into five ones. The total the three men ultimately paid is $12, as they get three ones back. So from the $12 the men paid, the owner receives $10 and the waiter receives the $2 difference. $15 - $3 = $10 + $2.

Qwail is the winner of this one. Please contact me In game for your prize. Thanks to everyone who participated. Those who were also correct are:
Sizzly
Loathe
Twittly
Carpaccio
Sorry if I have left anyone out.
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Chopzx/Chopzx-East on Emerald
Chopzx/Chopzx-West on Meridian
[Jun 21, 2013 3:43:26 PM] Show Printable Version of Post        Send Private Message [Link]  Go to top 
Dylan

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Re: Logical puzzles: work that brain Reply to this Post
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You are the king of The Cursed Isles and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You've got 1000 barrels of rum which you were planning to open for the celebration, but you find out that one of them is poisoned.

The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison.

You have over a thousand skellies and zombies at your disposal and just under 24 hours to determine which single bottle is poisoned.

You have a handful of prisoners... i mean pirates... about to be executed, and it would mar your celebration to have anyone else killed.

What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?



Solution: 10 prisoners must sample the wine. Bonus points if you worked out a way to ensure than no more than 8 prisoners die.

Number all bottles using binary digits. Assign each prisoner to one of the binary flags. Prisoners must take a sip from each bottle where their binary flag is set.


With ten people there are 1024 unique combinations so you could test up to 1024 bottles of wine.

Each of the ten prisoners will take a small sip from about 500 bottles. Each sip should take no longer than 15 seconds and should be a very small amount. Small sips not only leave more wine for guests. Small sips also avoid death by alcohol poisoning. As long as each prisoner is administered about a millilitre from each bottle, they will only consume the equivalent of about one bottle of wine each.

Each prisoner will have at least a fifty percent chance of living. There is only one binary combination where all prisoners must sip from the wine. If there are ten prisoners then there are ten more combinations where all but one prisoner must sip from the wine. By avoiding these two types of combinations you can ensure no more than 8 prisoners die.

Loathe be the winner of this one. Next answer coming up


Just as a matter of interest, why did you say this was hard?

Admittedly, it took me almost a minute to decide on ten.

First 30 seconds: over 1000 skellies available. Hard problem
Next 10 seconds: reread, realise handful of pirates are the ones to potentially die.
Next 18 seconds: solved problem.
Last second: undead can't die.
[Jun 21, 2013 5:13:55 PM] Show Printable Version of Post        Send Private Message [Link]  Go to top 
Chopzx

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Re: Logical puzzles: work that brain Reply to this Post
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Answer to the string burning Q

Solution: Light both the ends of the first string and one end of the second string. 30 minutes will have passed when the first string is fully burned, which means 30 minutes have burned off the second string. Light the end of the second string and when it is fully burned, 45 minutes will have passed.

Some people have difficulty grasping that when you light both ends of the first fuse, it will take 30 minutes to burn. Because the burning rate is random and unknown to you, you have no idea where the 30 minute mark is on the fuse. If you had an exact duplicate, then the 30 minute mark would be in the same place. It is probably not in the middle, but it is somewhere. If you burn both ends of a fuse it will not stop burning until it has reached this mark, which means 30 minutes is up.

The winner is Twittly. Please send me a tell in game for your prize
Thanks to those who participated
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Chopzx/Chopzx-East on Emerald
Chopzx/Chopzx-West on Meridian
[Jun 25, 2013 3:06:44 PM] Show Printable Version of Post        Send Private Message [Link]  Go to top 
Chopzx

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Re: Logical puzzles: work that brain Reply to this Post
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Ten pirates land on Hinga island. There they find lots of coconuts and a monkey. During their first day they gather coconuts and put them all in a community pile. After working all day they decide to sleep and divide them into ten equal piles the next morning.

That night one castaway wakes up hungry and decides to take his share early. After dividing up the coconuts he finds he is one coconut short of ten equal piles. He also notices the monkey holding one more coconut. So he tries to take the monkey's coconut to have a total evenly divisible by 10. However when he tries to take it the monkey conks him on the head with it and kills him.

Later another castaway wakes up hungry and decides to take his share early. On the way to the coconuts he finds the body of the first castaway, which pleases him because he will now be entitled to 1/9 of the total pile. After dividing them up into nine piles he is again one coconut short and tries to take the monkey's slightly bloodied coconut. The monkey conks the second man on the head and kills him.

One by one each of the remaining castaways goes through the same process, until the 10th person to wake up gets the entire pile for himself.

What is the smallest number of possible coconuts in the pile, not counting the monkeys?


Solution: 2519

The solution for the answer is the LCM (Lowest Common Multiple) of 10,9,8,7,6,5,4,3,2,1 -1. LCM would give the least number which is divisible by all of these number and subtracting one would give us the number of coconuts which were initially there.

Winner here is also Twittly
Ty for participating

Next Q coming up.
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Chopzx/Chopzx-East on Emerald
Chopzx/Chopzx-West on Meridian
[Jun 25, 2013 3:08:28 PM] Show Printable Version of Post        Send Private Message [Link]  Go to top 
Chopzx

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A stark raving mad king tells his 100 wisest men he is about to line them up and that he will place either a red or blue hat on each of their heads. Once lined up, they must not communicate amongst themselves. Nor may they attempt to look behind them or remove their own hat.

The king tells the wise men that they will be able to see all the hats in front of them. They will not be able to see the color of their own hat or the hats behind them, although they will be able to hear the answers from all those behind them.

The king will then start with the wise man in the back and ask "what color is your hat?" The wise man will only be allowed to answer "red" or "blue," nothing more. If the answer is incorrect then the wise man will be silently killed. If the answer is correct then the wise man may live but must remain absolutely silent.

The king will then move on to the next wise man and repeat the question.

The king makes it clear that if anyone breaks the rules then all the wise men will die, then allows the wise men to consult before lining them up. The king listens in while the wise men consult each other to make sure they don't devise a plan to cheat. To communicate anything more than their guess of red or blue by coughing or shuffling would be breaking the rules.

What is the maximum number of men they can be guaranteed to save?


PLEASE SEND ME A PM WITH ANSWER, PIRATE NAME, AND NAME THE SUBJECT OF THE PM AS "King Wise Men".
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Chopzx/Chopzx-East on Emerald
Chopzx/Chopzx-West on Meridian
[Jun 25, 2013 3:14:39 PM] Show Printable Version of Post        Send Private Message [Link]  Go to top 
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