Car talk plaza puzzler revisited

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Breaking the Sound Barrier… on Horseback!
RAY: Long before the advent of the train, travelers on horseback regularly broke the sound barrier. How'd they do it?

The inspiration for this puzzler was sent in by a fellow named Pierro Martilucci.

Nowadays, we're very accustomed to high-speed travel. We have passenger planes that go close to 500 mph, and even our cars can go well over 100 mph.

But until the advent of the train, the fastest that anyone could travel, unless you either fell off a cliff or were shot from a cannon, was as fast as a horse could carry or pull you. And yet, some of the people on horseback or driving a team of horses broke the sound barrier on a regular basis.

How did they do it? And by the way, there are hints in here!

 

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Spoiler: Answer

They broke the sound barrier when they "cracked" their whip.

The "crack" sound is essentially the "sonic boom" attained by the speed of its tip.

Rawhide, Frankie Laine (1958)

 

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Breaking the Sound Barrier… on Horseback!
RAY: Long before the advent of the train, travelers on horseback regularly broke the sound barrier. How'd they do it?

The inspiration for this puzzler was sent in by a fellow named Pierro Martilucci.

Nowadays, we're very accustomed to high-speed travel. We have passenger planes that go close to 500 mph, and even our cars can go well over 100 mph.

But until the advent of the train, the fastest that anyone could travel, unless you either fell off a cliff or were shot from a cannon, was as fast as a horse could carry or pull you. And yet, some of the people on horseback or driving a team of horses broke the sound barrier on a regular basis.

How did they do it? And by the way, there are hints in here!

Answer:
RAY: We discovered this phenomenon in the locker room in high school, with a wet towel. We would wet the end of a towel and you'd snap it, and it would make a loud “crack!”.

The tip of the wet towel when it snapped at the end was going faster than the speed of sound, and that's why it hurt so much when we caught somebody in the butt. But the end of a whip is also traveling faster than the speed of sound.

It's creating a little sonic boom. Pretty cute, huh?

 

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The Loose Caboose
RAY: Here’s a puzzler of yesteryear.

Imagine, if you will, a long freight train. As the kind, you see out West with a couple of hundred cars getting ready to leave the train yard. The engineer opens the throttle and the train starts to pull away from the yard. Then they realize that the caboose has a problem. The brake is frozen on one of the wheels of the caboose, and the wheel is being dragged so there are sparks and smoke.

Someone standing there says, "Stop the train." So, they manage to signal to the engineer, to stop the train. Well, they can't fix it, so they just cut the caboose loose. They remove it and they give him the go ahead. They wave him. You know. Go ahead. He gives it the throttle. The train doesn't move.

He gives it more throttle, it doesn't move. He gives it more and what's happening in the train isn't moving, but his wheels are spinning. There's nothing wrong with any of the remaining cars and there's nothing wrong with the engine, but there is something wrong with the engineer.

The question is what's wrong with this picture?

 

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He hasn't released the brake...?

 

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The Loose Caboose
RAY: Here’s a puzzler of yesteryear.

Imagine, if you will, a long freight train. As the kind, you see out West with a couple of hundred cars getting ready to leave the train yard. The engineer opens the throttle and the train starts to pull away from the yard. Then they realize that the caboose has a problem. The brake is frozen on one of the wheels of the caboose, and the wheel is being dragged so there are sparks and smoke.

Someone standing there says, "Stop the train." So, they manage to signal to the engineer, to stop the train. Well, they can't fix it, so they just cut the caboose loose. They remove it and they give him the go ahead. They wave him. You know. Go ahead. He gives it the throttle. The train doesn't move.

He gives it more throttle, it doesn't move. He gives it more and what's happening in the train isn't moving, but his wheels are spinning. There's nothing wrong with any of the remaining cars and there's nothing wrong with the engine, but there is something wrong with the engineer.

The question is what's wrong with this picture?

Answer:
RAY: When a locomotive is pulling cars, each car is attached to the one in front of it and behind it by a coupling, but the couplings aren't rigid. They're, in fact, sloppy.

So when a long freight train pulls out of a yard, before it takes off, it will frequently back up to compress all the couplings and then when it takes off, one car at a time begins to move and it's quite a while, in fact, before the caboose begins to move.

But in this situation, the train was stopped. He did that backing up thing. I failed to mention that in the statement of the puzzler.

The train is halted because the brake is stuck and because it's stuck, the caboose is in a sense pulling the train from the other end. So, now all the couplings are all stretched out. They remove the caboose, but the guy doesn't back up.

So he's going to try to move the last car while he's trying to move the first car and the train is just too heavy and he doesn't have enough friction between the wheels on the track.

If a train is too long, it can't really pull from a dead stop all the cars that you see behind it sometimes. So, the little engine that couldn't.

 

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Chemistry Test
RAY: I shamelessly stole this from Joseph Rayle from Durham, North Carolina.

Two undergraduate chemistry students at a major university had a highly successful semester in an introductory chemistry class. So their confidence is high, so high in fact that they decide to blow off their reading period, and they go to a fraternity party in a town quite a distance away and they have a pretty good time. So good in fact that they don't make it back in time for their final exam.

In a panic, however, they devise a plan. They agreed to tell the professor that they had a flat tire and this prevented their returning in time to take the exam. They pleaded with him, "Let us take the exam, please, this could ruin us, we promise nothing like this will ever happen again." The professor agrees and tells them to return the next morning. The two return the following morning, and the professor gives them their exam but decides he isn't going to hang around. He has them leave their books and backpacks in the office and sends them to different rooms to take their exams. The test consists of one five-point question - some molarity problem - and each, smiling confidently, answers the question. Then they turn the page, and the next question is a ninety-five-point question.

And our question is: What is the question?

 

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Spoiler: My Guess...?

What really happened when you missed the exam...?

More specifically, "Which tire was flat?"

 

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Chemistry Test
RAY: I shamelessly stole this from Joseph Rayle from Durham, North Carolina.

Two undergraduate chemistry students at a major university had a highly successful semester in an introductory chemistry class. So their confidence is high, so high in fact that they decide to blow off their reading period, and they go to a fraternity party in a town quite a distance away and they have a pretty good time. So good in fact that they don't make it back in time for their final exam.

In a panic, however, they devise a plan. They agreed to tell the professor that they had a flat tire and this prevented their returning in time to take the exam. They pleaded with him, "Let us take the exam, please, this could ruin us, we promise nothing like this will ever happen again." The professor agrees and tells them to return the next morning. The two return the following morning, and the professor gives them their exam but decides he isn't going to hang around. He has them leave their books and backpacks in the office and sends them to different rooms to take their exams. The test consists of one five-point question - some molarity problem - and each, smiling confidently, answers the question. Then they turn the page, and the next question is a ninety-five-point question.

And our question is: What is the question?

Answer:
RAY: The second question, worth 95 points on the exam, was: “Which tire was flat?”

 

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More Matchstick Mathematics
RAY: Go out and get yourself 16 matchsticks. You're going to use the matchsticks to make the following Roman numeral sequence. One, then two matchsticks to make a plus sign. Plus Roman numeral two. Plus Roman numeral three. Plus Roman numeral four, which is not "IV," but, in this case, "IIII."

[ For the Car Talk Puzzler Psychic Friends Network, that equation would be: I + II + III + IIII ]

If you add this up, one plus two plus three plus four, adds up to 10.

The question is, can you move one matchstick, without removing it, still using them all -- and make that equal to four?

 

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Spoiler: My Guess

- I - II + III + IIII

 

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More Matchstick Mathematics
RAY: Go out and get yourself 16 matchsticks. You're going to use the matchsticks to make the following Roman numeral sequence. One, then two matchsticks to make a plus sign. Plus Roman numeral two. Plus Roman numeral three. Plus Roman numeral four, which is not "IV," but, in this case, "IIII."

[ For the Car Talk Puzzler Psychic Friends Network, that equation would be: I + II + III + IIII ]

If you add this up, one plus two plus three plus four, adds up to 10.

The question is, can you move one matchstick, without removing it, still using them all -- and make that equal to four?

Answer:
RAY: The challenge is to move and reuse one matchstick to make this sum equal not to 10, but to four. And what you do is you take the plus sign between the one and the two, take the vertical matchstick, and put it horizontally in front of the one, so now the thing reads minus one, minus two, plus three plus four equals four! A lot of people have trouble with this because of the idea of putting a negative sign in front.

 

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Busting the Midnight Siphonist
RAY: It took place in the early 1970s, during the first gas crunch when there were long lines at gas stations, and Toyotas started looking really good to people who owned Detroit gas guzzlers. My friend Maryann lived in a rural neighborhood in upstate New York, and someone was sneaking around late at night in the inky shadows, siphoning gasoline, while the honest people were asleep. Maryann and the sheriff got together and hatched a plan to catch the thief. It involved using Maryann's car, and its full tank of gasoline as the bait.

Unlike many of her neighbors, Maryann did not own a locking gas cap, so her tank was very siphonable. The idea wasn't to catch the thief with a secret alarm, hidden cameras, or anything like that. They would catch the thief just by allowing him to siphon the gas and take it home for use in his own car.

The thief did strike and siphon her gas, and it was the end of the gas thefts.

The question is, what trap did they lay, and what was it about Maryann's car that made it easy to figure out who the gas thief was?

 

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Spoiler: Maybe...?

Her car ran on diesel fuel...?

 

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Busting the Midnight Siphonist
RAY: It took place in the early 1970s, during the first gas crunch when there were long lines at gas stations, and Toyotas started looking really good to people who owned Detroit gas guzzlers. My friend Maryann lived in a rural neighborhood in upstate New York, and someone was sneaking around late at night in the inky shadows, siphoning gasoline, while the honest people were asleep. Maryann and the sheriff got together and hatched a plan to catch the thief. It involved using Maryann's car, and its full tank of gasoline as the bait.

Unlike many of her neighbors, Maryann did not own a locking gas cap, so her tank was very siphonable. The idea wasn't to catch the thief with a secret alarm, hidden cameras, or anything like that. They would catch the thief just by allowing him to siphon the gas and take it home for use in his own car.

The thief did strike and siphon her gas, and it was the end of the gas thefts.

The question is, what trap did they lay, and what was it about Maryann's car that made it easy to figure out who the gas thief was?

Answer:
RAY: Maryann's car was a Saab. And from 1959, I think, to 1969, Saab made a two-stroke engine. When the gas thief put the mixture of gas and oil from that car into his Chevy or whatever he drove, the trail of smoke he left behind allowed the sheriff to follow him right home, and arrest him.

 

[returntosender]

Your still posting this.

 

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The most recent puzzle is too automobile-specific.

 

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The Young Mathematician
Several hundred years ago, somewhere in Europe, in a classroom, a teacher is assigning the students some busy work as a kind of punishment because the class has been misbehaving.

The teacher says "Okay, wise guys, I want you to add up all the numbers between one and 100. I.e. one plus two, plus three, six. Four, plus five, plus six, plus seven."

As you can see, it begins to get tough. And don't forget, they were little kids, they could barely even make the numbers! After about a minute or so, one of the kids raises his hand and says, I have the answer.

And the teacher says, "The heck you do!"

But the student says, "The answer is 5050." And indeed that was the answer. The question is, how did he do it so quickly?

And part two for extra credit is, who was this kid? (He was a famous mathematician.) What's his name?

 

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Spoiler: How did he do it so quickly?

For any natural number n,
1 + 2 + 3 + ... + n = ( n x (n + 1)) ÷ 2

It was discovered by one Carl Friedrich Gauss.
(I had to look him up.)

 

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The Young Mathematician
Several hundred years ago, somewhere in Europe, in a classroom, a teacher is assigning the students some busy work as a kind of punishment because the class has been misbehaving.

The teacher says "Okay, wise guys, I want you to add up all the numbers between one and 100. I.e. one plus two, plus three, six. Four, plus five, plus six, plus seven."

As you can see, it begins to get tough. And don't forget, they were little kids, they could barely even make the numbers! After about a minute or so, one of the kids raises his hand and says, I have the answer.

And the teacher says, "The heck you do!"

But the student says, "The answer is 5050." And indeed that was the answer. The question is, how did he do it so quickly?

And part two for extra credit is, who was this kid? (He was a famous mathematician.) What's his name?

Answer:
Have I got an answer for you!

Now I'm sure everyone will attribute this incorrectly to our pal, Al Einstein. But I gave a hint, a big hint!

That it was hundreds of years ago.

I don't even know if it was hundreds of years ago. In any event, it was the German mathematician, Carl Friedrich Gauss. Gauss, as a child, used to amaze his classmates and his school teacher with the logic he used. He said, "Look, I took the first number in the last number, the first being one and the last being 100. I add them up and I got 101. The next one next pair, I added two and 99."

So basically what he did was he wrote the numbers in ascending order on one line, and right below me wrote the numbers in descending order.

So you add the first pair of numbers and get 101. Then the next pair is 99 + 2. And you get 101. 98 + 3 is also 101.

He said, "Gee, every line obviously comes out to 101. So I had 100 one 101s, which is 10,100. But since I used each number twice, I divided by two and got 5050."

And of course, he went on to become a renowned mathematician.