Puzzles and Conundrums

[Taleung]

There’s an airplane with 100 seats, and there are 100 ticketed passengers each with an assigned seat. They line up to board in some random order. However, the first person to board is the worst person alive, and just sits in a random seat, without even looking at his boarding pass. Each subsequent passenger sits in his or her own assigned seat if it’s empty, but sits in a random open seat if the assigned seat is occupied. What is the probability that you, the hundredth passenger to board, finds your seat unoccupied?

 

50%

[Pdoggg]

50%

 

Correctomundo!  

 

Given how the other passengers are choosing their seats, you have a 50 percent chance of finding your assigned seat empty. The solution may seem counterintuitive — at first glance it seems like there will be a growing wave of wrong-seat-sitters, mayhem will ensue, fights will break out, and the odds that you get your assigned seat will plummet. But really, there are only two seat assignments you care about: yours and the one meant for the world’s worst passenger, the guy who boards first. These are the only two seats that can be the final unoccupied seat. This can be proven by contradiction: If the seat belonging to the Nth passenger (where N isn’t you or the first passenger) is the final open seat, then it was also open when the Nth passenger boarded, and she would’ve taken it then, so it can’t be the final open seat. Q.E.D. The two potential final seats — your and the first guy’s — are otherwise identical, so when you board, there’s a 50-50 chance yours is the one open at the end.

Another tack is a sort-of induction argument, starting with a smaller plane and seeing what happens to the solution when it gets larger. Imagine the plane has just two seats. The world’s worst person will clearly take your seat half the time, leaving you with your assigned seat half the time. Now imagine the plane has three seats. The world’s worst person will take your seat a third of the time. Another third of the time he’ll take the other passenger’s seat, in which case that other passenger will take your seat half the time. Your seat is taken ⅓+(⅓*½)=½ the time. Again, you get your assigned seat half the time. And so on and so forth. The answer is 50 percent regardless of how large the plane is.

[Pdoggg]

Here are four different coded messages. Each has a different encryption scheme and they progress, I think, from easiest to toughest to crack. Submit the decrypted messages as your answers.

1. A zsnw kmuuwkkxmddq kgdnwv lzw XanwLzajlqWayzl Javvdwj!


2. xckik acvlbeg oz mmqn xnlautw. gzag, mwcht, kbjzh… ulw cpeq edr mom dhqx lksxlioil?


3. hy vg nw rh ev pr is or tf?

[Pdoggg]

Two players go on a hot new game show called “Higher Number Wins.” The two go into separate booths, and each presses a button, and a random number between zero and one appears on a screen. (At this point, neither knows the other’s number, but they do know the numbers are chosen from a standard uniform distribution.) They can choose to keep that first number, or to press the button again to discard the first number and get a second random number, which they must keep. Then, they come out of their booths and see the final number for each player on the wall. The lavish grand prize — a case full of gold bullion — is awarded to the player who kept the higher number. Which number is the optimal cutoff for players to discard their first number and choose another? Put another way, within which range should they choose to keep the first number, and within which range should they reject it and try their luck with a second number?

[Pdoggg]

A scandal in the crossword world...

 

 

A group of eagle-eyed puzzlers, using digital tools, has uncovered a pattern of copying in the professional crossword-puzzle world that has led to accusations of plagiarism and false identity.

 

Since 1999, Timothy Parker, editor of one of the nation’s most widely syndicated crosswords, has edited more than 60 individual puzzles that copy elements from New York Times puzzles, often with pseudonyms for bylines, a new database has helped reveal. The puzzles in question repeated themes, answers, grids and clues from Times puzzles published years earlier. Hundreds more of the puzzles edited by Parker are nearly verbatim copies of previous puzzles that Parker also edited. Most of those have been republished under fake author names.

 

Nearly all this replication was found in two crosswords series edited by Parker: the USA Today Crossword and the syndicated Universal Crossword. (The copyright to both puzzles is held by Universal Uclick, which grew out of the former Universal Press Syndicate and calls itself “the leading distributor of daily puzzle and word games.”) USA Today is one of the country’s highest-circulation newspapers, and the Universal Crossword is syndicated to hundreds of newspapers and websites.

 

On Friday, a publicity coordinator for Universal Uclick, Julie Halper, said the company declined to comment on the allegations. FiveThirtyEight reached out to USA Today for comment several times but received no response.

 

UPDATE (March 7, 6:08 p.m.): Since the publication of this article, Universal Uclick and USA Today have each said that Timothy Parker will be stepping back from his role creating puzzles for the two publishers while an investigation is conducted.

http://fivethirtyeight.com/features/a-plagiarism-scandal-is-unfolding-in-the-crossword-world/

[Pdoggg]

 

SEOUL, South Korea — Computer, one. Human, zero.

 

A Google computer program stunned one of the world’s top players on Wednesday in a round of Go, which is believed to be the most complex board game ever created.

 

The match — between Google DeepMind’s AlphaGo and the South Korean Go master Lee Se-dol — was viewed as an important test of how far research into artificial intelligence has come in its quest to create machines smarter than humans.

 

“I am very surprised because I have never thought I would lose,” Mr. Lee said at a news conference in Seoul. “I didn’t know that AlphaGo would play such a perfect Go.”

 

Mr. Lee acknowledged defeat after three and a half hours of play.

 

Demis Hassabis, the founder and chief executive of Google’s artificial intelligence team DeepMind, the creator of AlphaGo, called the program’s victory a “historic moment.”

 

The match, the first of five scheduled through Tuesday, took place at a Seoul hotel amid intense news media attention. Hundreds of reporters, many of them from China, Japan and South Korea, where Go has been played for centuries, were there to cover it. Tens of thousands of people watched the contest live on YouTube.

 

Go is a two-player game of strategy said to have originated in China 3,000 years ago. Players compete to win more territory by placing black and white “stones” on a grid measuring 19 squares by 19 squares.

 

The play is more complex than chess, with a far greater possible sequence of moves, and requires superlative instincts and evaluation skills. Because of that, many researchers believed that mastery of the game by a computer was still a decade away.

 

Before the match, Mr. Lee said he could win 5-0 or 4-1, predicting that computing power alone could not win a Go match. Victory takes “human intuition,” something AlphaGo has not yet mastered, he said.

But after reading more about the program he became less upbeat, saying that AlphaGo appeared able to imitate human intuition to a certain degree and predicting that artificial intelligence would eventually surpass humans in Go.

 

AlphaGo posed Mr. Lee a unique challenge. In a human-versus-human Go match, which typically lasts several hours, the players “feel” each other and evaluate styles and psychologies, he said.

 

“This time, it’s like playing the game alone,” Mr. Lee said on the eve of the match. “There are mistakes humans make because they are humans. If that happens to me, I can lose a match.”

 

To researchers who have been using games as platforms for testing artificial intelligence, Go has remained the great challenge since the I.B.M.-developed supercomputer Deep Blue beat the world chess champion Garry Kasparov in 1997.

 

“Really, the only game left after chess is Go,” Mr. Hassabis said on Wednesday.

www.nytimes.com/2016/03/10/world/asia/google-alphago-lee-se-dol.html

[Pdoggg]

50 State Challenge Minefield.

 

If there were border lines it would be quite easy. This is not.

 

If you pick the order of the states, it would be easy.

 

But if Delaware pops up early you are fooked.

 

http://www.sporcle.com/games/mhershfield/us-states-no-outlines-minefield

[Tomcat]

[bumblebee]

Mmm....

[TEXASMAC]

The word "THE" is used twice in a row !

[bumblebee]

The word "THE" is used twice in a row !

Well spotted TM.

[Pdoggg]

You and four ladyboys find a 1000 baht note on the floor of Lita Bar. None of you have change, so you agree to play a game of chance to divide the money probabilistically. The five of you sit around a table. The game is played in turns. Each turn, one of three things can happen, each with an equal probability: The 1000 baht note can move one position to the left, one position to the right, or the game ends and the person with the 1000 baht in front of him or her wins the game. You have the biggest dick, so the1000 baht starts in front of you. What are the chances you win the money?

[Pdoggg]

Here's an easy one.

 

[Tomcat]

18..... is my answer...sorry for the late reply

 

[Tomcat]

This was in New Scientist quiz a few weeks back and so 

What is remarkable about the following sentence....................

 

i am not very happy acting pleased

whenever prominent scientists

overmagnify intellectual enlightenment

 

[stoolpusher]

10 for me ( actual squares , no oblongs )

[sydneyjohn57]

I agree with Tomcat = 18

8 squares of 1x1

5 squares of 2x2

4 squares of 3x3

1 square of 4x4

[Tomcat]

the 4 of 3x3 are the ones that catch you out.. i missed them firstly

and now.....

Im now trying to figure " the highest number wins " puzzle , these things are tricky and this one is just that....im using playing cards to help figure it out

[Tomcat]

On 3/6/2016 at 10:42 AM, Pdoggg said:

Two players go on a hot new game show called “Higher Number Wins.” The two go into separate booths, and each presses a button, and a random number between zero and one appears on a screen. (At this point, neither knows the other’s number, but they do know the numbers are chosen from a standard uniform distribution.) They can choose to keep that first number, or to press the button again to discard the first number and get a second random number, which they must keep. Then, they come out of their booths and see the final number for each player on the wall. The lavish grand prize — a case full of gold bullion — is awarded to the player who kept the higher number. Which number is the optimal cutoff for players to discard their first number and choose another? Put another way, within which range should they choose to keep the first number, and within which range should they reject it and try their luck with a second number?

 

My Answer

If you are on or over 0.5 you hold  .. under and press the button

[Pdoggg]

TC was the first to guess the number of squares and was verified by SJ57. Well done!

16 hours ago, Tomcat said:

My Answer

If you are on or over 0.5 you hold  .. under and press the button

This is an extremely difficult puzzle perhaps the toughest one posted so far.  

The “obvious” solution is to use a cutoff of 0.5, throwing away your number in exchange for another if it’s less than 0.5, and keeping it if it’s greater than that, since that strategy will yield the highest average final number. But that isn’t the optimal cutoff.

Let C be the optimal cutoff the players use. The key observation is that if the first number revealed is exactly C, then the probability of winning by keeping C equals the probability of winning by pressing the button again — you are indifferent. We can compute each of these probabilities, keeping in mind that the other player is also using C as their cutoff.

(The answer won't paste correctly so the details are at the bottom of the article in this link  https://fivethirtyeight.com/features/can-you-win-this-hot-new-game-show/. )

0.618034..... is the answer.
Note that this cutoff is the golden ratio minus one, known as the golden ratio conjugate. So using the golden ratio gives the best chance to win the gold bullion!

[Pdoggg]

On 8/24/2020 at 2:17 AM, Tomcat said:

This was in New Scientist quiz a few weeks back and so 

What is remarkable about the following sentence....................

 

i am not very happy acting pleased

whenever prominent scientists

overmagnify intellectual enlightenment

 

The number of letters in each word in the sentence increases by 1 as the sentence goes on starting with i which has 1 letter to enlightenment which has 13 letters. 

[Tomcat]

its correct PD , i must admit i didnt figure it when i see it

[Tomcat]

6 hours ago, Pdoggg said:

 

0.618034..... is the answer.
Note that this cutoff is the golden ratio minus one, known as the golden ratio conjugate. So using the golden ratio gives the best chance to win the gold bullion!

that was a tough one ...if i didnt have a day job i might have come closer  ...i was using pack of playing cards to try to figure it out 

[Tomcat]

NEW puzzle

Many Scientists use this as a password ..... O,T,T,F,F ... as its the beginning of an infinite sequence with a simple rule ...and you wont ever forget it no matter how drunk you are

what are the next two letters of the sequence

 

[bumblebee]

4 hours ago, Tomcat said:

NEW puzzle

Many Scientists use this as a password ..... O,T,T,F,F ... as its the beginning of an infinite sequence with a simple rule ...and you wont ever forget it no matter how drunk you are

what are the next two letters of the sequence

 

I’ll pass on this one, as it’s a puzzle I use regularly in class and it really bugs the students until they cop it.