Car talk plaza puzzler revisited

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Stack the Deck
RAY: Let's say you have two ordinary decks of playing cards, minus the jokers. So, you have a deck of 52 cards and another deck of 52 cards.

Same color? The backs of them are red. And the other sides, the business sides are the same. So you take them and you shuffle them up--mix them all up as best you can.

Both decks together, so one hundred four cards.

And then you divide them into two equal piles. So, you've got a pile of 52 on one side of the table, and a pile of 52 on the other side of the table. Are you with me so far?

So, I've shuffled 104 cards together, and I've split them back into two piles of 52 each, and I've got one pile here on my left, and one pile to my right.

What are the chances that the number of red cards in pile A equals the number of black cards in pile 2? That's part one of the question. And then part two of the question: how many cards would you have to look at to be certain of your answer?

Answer:
The chances are: One hundred percent!

Imagine if you - let's say by some luck, you shuffled up all these cards and all the red cards wound up in one pile, we'll call that pile A. And for simplicity's sake, we'll call the other pile, pile B, and all the black cards wound up in that. Then you would say, well, certainly the number of red cards in deck A, or pile A, equals the number of black cards in pile B. Now, I ask you to construct a scenario where it wouldn't be the case, always.

How about one and 51? Take a card out of pile A and donate it to pile B--but when you do that, you must reciprocate and take a black card from pile B and donate it to pile A. Therefore you have 51 and one, and 51 and one, and no matter how you do this if you wind up with 52 cards in each pile the number red cards in pile A will equal the number of black cards in pile 2.

And part B of the question: How many cards do you have to look at to verify your answer?

None.

You think it's great because you got the answer. If you hadn't gotten the answer, you'd be all over this thing.

 

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Bobo's "Don't Look Back" Tour
The company that Bobo works for just finished a new product. They wanted to promote it across the country. Bobo was asked to travel by car to each of the 48 contiguous U.S. states to promote the product. He was told that he could visit each state in whatever order he chose, but the company wanted him to start in Delaware, at their headquarters.

They asked that he visit each state only once. He could not go back into a state he had already visited--this was the "Don't Look Back" product tour. So, Bobo sat down at his desk and began to plan his trip.

He realized immediately that it was going to be one long car trip. At that moment, his boss stopped by and said, "Hey, I'm going to join you when you reach your last state. I was born there and I've been looking for a reason to go back and visit. You can leave your rental car there, and I'll fly you back in my private jet."

Since Bobo hadn't planned his trip yet, how did his boss know which state was going to be Bobo's last state? And, which state would that be?

 

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Spoiler: State?

Maryland

Spoiler: Why?

There are only three states that border Delaware.
He will need New Jersey to head into New England.
He will need Pennsylvania to exit New England.
That only leaves Maryland as the state by which he returns to Delaware.
(Because of New York, he will have to drive in Canada to avoid recrossing some states in New England...)

If New England was the last leg of his trip, New Jersey & Maryland would be reversed.

 

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Bobo's "Don't Look Back" Tour
The company that Bobo works for just finished a new product. They wanted to promote it across the country. Bobo was asked to travel by car to each of the 48 contiguous U.S. states to promote the product. He was told that he could visit each state in whatever order he chose, but the company wanted him to start in Delaware, at their headquarters.

They asked that he visit each state only once. He could not go back into a state he had already visited--this was the "Don't Look Back" product tour. So, Bobo sat down at his desk and began to plan his trip.

He realized immediately that it was going to be one long car trip. At that moment, his boss stopped by and said, "Hey, I'm going to join you when you reach your last state. I was born there and I've been looking for a reason to go back and visit. You can leave your rental car there, and I'll fly you back in my private jet."

Since Bobo hadn't planned his trip yet, how did his boss know which state was going to be Bobo's last state? And, which state would that be?

Answer:
RAY: He winds up in the one state that borders only one other state -- the great state of Maine, which only borders New Hampshire and, of course, Canada.

And the Atlantic Ocean.

 

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How Does Pork Chop Boy Drive To Work?
RAY: The inspiration for this puzzler was sent in by Warner Grenady. Of course, I had to add some obfuscatory details, and I personalized it a little bit.

Some of you might remember our nephew Matt, whom we called "Pork Chop Boy," because his social life was so bad, he had to tie a pork chop around his neck even to get the dog to play with him.

Anyway, some years ago he dislocated his right shoulder playing chess. It was "strip chess" actually, but, we don't have to go into that. His shoulder hurt so much that he couldn't move the shifter on his automatic transmission. He tried to reach over and shift with the other hand, but twisting in the seat hurt even more.

But, Pork Chop Boy needed to drive to work every day, and he didn't have any way to get there. Tommy said, "No problem. You can use my car." He did, and he had no problem driving Tommy's car to work-- yet, he couldn't shift his own automatic transmission car.

The question is, which one of Tommy's jalopies did Matt use to get to work, and why?

 

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Spoiler: My Guess

Tommy's car is configured for British/RHD steering.

 

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How Does Pork Chop Boy Drive To Work?
RAY: The inspiration for this puzzler was sent in by Warner Grenady. Of course, I had to add some obfuscatory details, and I personalized it a little bit.

Some of you might remember our nephew Matt, whom we called "Pork Chop Boy," because his social life was so bad, he had to tie a pork chop around his neck even to get the dog to play with him.

Anyway, some years ago he dislocated his right shoulder playing chess. It was "strip chess" actually, but, we don't have to go into that. His shoulder hurt so much that he couldn't move the shifter on his automatic transmission. He tried to reach over and shift with the other hand, but twisting in the seat hurt even more.

But, Pork Chop Boy needed to drive to work every day, and he didn't have any way to get there. Tommy said, "No problem. You can use my car." He did, and he had no problem driving Tommy's car to work-- yet, he couldn't shift his own automatic transmission car.

The question is, which one of Tommy's jalopies did Matt use to get to work, and why?

Answer:
RAY: It wasn't his sleek black beauty because that was what? In the crusher.

It wasn't his MGTD because you need three arms to drive that.

It was his '63 Dodge Dart because it had a push button shifter located on the left side of the dashboard.

All you had to do was press a button, and you'd be in drive. Press another button, and you would be in either reverse or park, and that's all you needed. Matt was able to get to work, earn some money and stay out of the poor house.

 

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Tire mounting... with but a few letters.
RAY: I'm going to have winter tires put on my car. I bought four of them. I'm moving soon, and since I'll be taking the car to a different shop to have them changed back next spring, the tires have to be marked so they can be put back where they belong, i.e., where they came from. So the left front has to go the left front, the right front has to go there, and so on.

When I take them off, I'm going to ask the people at the gas station to mark them with letters.

The question is, what's the smallest number of letters needed to mark my tires to guarantee that all four of them can get correctly installed with no chance of error or ambiguity in the spring?

 

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Tire mounting... with but a few letters.

Spoiler: My Approach

q p
d b

 

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Tire mounting... with but a few letters.
RAY: I'm going to have winter tires put on my car. I bought four of them. I'm moving soon, and since I'll be taking the car to a different shop to have them changed back next spring, the tires have to be marked so they can be put back where they belong, i.e., where they came from. So the left front has to go the left front, the right front has to go there, and so on.

When I take them off, I'm going to ask the people at the gas station to mark them with letters.

The question is, what's the smallest number of letters needed to mark my tires to guarantee that all four of them can get correctly installed with no chance of error or ambiguity in the spring?

Answer:
RAY: The answer is two. Two letters and each is used twice. The two letters are L and F.

Here's how the tires would be marked. By the way, you could do this in different ways, and you could use different letters, but this works.

The left front tire would be marked LF. The other front tire would simply be marked F.

The left rear tire would just be marked L.

And the fourth tire, which is the right rear, wouldn't be marked at all.

 

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A Magnetizing Dinner Chez Magliozzi
RAY: Picture this scene: A family dinner with the extended Magliozzi clan. Lots of people, lots of food, and of course, lots of noise. Suddenly above the cacophony, my usually quiet wife made herself heard.

'Check this out!' she shouted. 'My knife and fork are stuck to each other, kind of like they are magnetized.' Well, sure enough the knife was indeed magnetized. In fact, it was such a strong magnet, she was able to pick up my entire set of keys with that knife. (She had dropped my keys into the soup, but that's another story altogether.)

Then one of the boys figured out that his knife was magnetized too, but the polarity was the reverse of hers. We all puzzled over this phenomenon for a while, until my niece offered an explanation. When we checked out her theory, we discovered that she was right. What was her theory?

Here's the hint: We stuck Tommy with the check that day!

 

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A Magnetizing Dinner Chez Magliozzi
RAY: Picture this scene: A family dinner with the extended Magliozzi clan. Lots of people, lots of food, and of course, lots of noise. Suddenly above the cacophony, my usually quiet wife made herself heard.

'Check this out!' she shouted. 'My knife and fork are stuck to each other, kind of like they are magnetized.' Well, sure enough the knife was indeed magnetized. In fact, it was such a strong magnet, she was able to pick up my entire set of keys with that knife. (She had dropped my keys into the soup, but that's another story altogether.)

Then one of the boys figured out that his knife was magnetized too, but the polarity was the reverse of hers. We all puzzled over this phenomenon for a while, until my niece offered an explanation. When we checked out her theory, we discovered that she was right. What was her theory?

Here's the hint: We stuck Tommy with the check that day!

Answer:
RAY: Remember the hint? We stuck Tommy with the check because... we were out to dinner.

It wasn't a family dinner at home, we were at a restaurant. And restaurants have such large losses of silverware, that they throw into their trash receptacle an enormous magnet so that when silverware is mistakenly thrown into the trash can, the forks, spoons, and knives all get stuck to this magnet, and if it's on there long enough it gets pretty magnetized.

So that's how it happened. So the next time you're at a restaurant you can do a little parlor trick. Find a utensil that's magnetized, and you can pick up somebody's keys and drop their keys in their soup.

 

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The Extra 40 Pounds...
RAY: This came from a fellow named Josh Kokendolfer who says, "This is a true story”:

It was a brisk December morning. A co-worker and I had a simple job to do that day: clean out a job site and take the trash to the local landfill. And we had an F-350 pickup that was outfitted with a dump truck bed. We filled it up and headed out. When we arrived at the landfill we pulled the truck onto the scale that weighed our vehicle and the woman in the office waved us through.

We unloaded and headed back out to the scale. Once again our truck was weighed. Before getting into the truck I noticed that one of the back tires was low. I decided to stop at one of the local gas stations to check it out and fill all the tires just in case.

After lunch, we loaded the truck a second time at the site and headed back to the landfill. Everything went just like the first time. After we were weighed on exiting, I went to pay the bill. My co-worker looked at the paperwork and noticed something strange.

The first time we left we weighed 6,480 lbs. And the second time we exited we weighed 6,440 lbs - a difference of 40 lbs. We were being charged for an extra 40 pounds of trash that we didn't have. I immediately complained to the office manager. She grinned and said, "There's nothing wrong with our scales." Well, if that's the case, what happened?

 

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Spoiler: My Guess...

They left their full lunch boxes in the truck, the first time?

 

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The Extra 40 Pounds...
RAY: This came from a fellow named Josh Kokendolfer who says, "This is a true story”:

It was a brisk December morning. A co-worker and I had a simple job to do that day: clean out a job site and take the trash to the local landfill. And we had an F-350 pickup that was outfitted with a dump truck bed. We filled it up and headed out. When we arrived at the landfill we pulled the truck onto the scale that weighed our vehicle and the woman in the office waved us through.

We unloaded and headed back out to the scale. Once again our truck was weighed. Before getting into the truck I noticed that one of the back tires was low. I decided to stop at one of the local gas stations to check it out and fill all the tires just in case.

After lunch, we loaded the truck a second time at the site and headed back to the landfill. Everything went just like the first time. After we were weighed on exiting, I went to pay the bill. My co-worker looked at the paperwork and noticed something strange.

The first time we left we weighed 6,480 lbs. And the second time we exited we weighed 6,440 lbs - a difference of 40 lbs. We were being charged for an extra 40 pounds of trash that we didn't have. I immediately complained to the office manager. She grinned and said, "There's nothing wrong with our scales." Well, if that's the case, what happened?

Answer:
RAY: The reason the truck weighed 40 pounds less is that it had burned 40 pounds of gas or about six gallons.

 

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What Do These Eight Words Have in Common?
RAY: This is a word puzzler sent in by a fellow named Bob Dinger.

Each and every word in this list has the same unusual uniqueness in common. Here are the words:

Assess
Banana
Dresser
Grammar
Potato
Revive
Uneven
Voodoo

And here's a hint. If I left one of the words off the list, it wouldn't affect the answer. What do these words have in common?

 

[Sabertooth]

Spoiler: My Observation

If you drop the first letter, they are all palindromes.

 

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What Do These Eight Words Have in Common?
RAY: This is a word puzzler sent in by a fellow named Bob Dinger.

Each and every word in this list has the same unusual uniqueness in common. Here are the words:

Assess
Banana
Dresser
Grammar
Potato
Revive
Uneven
Voodoo

And here's a hint. If I left one of the words off the list, it wouldn't affect the answer. What do these words have in common?

Answer:
RAY: The answer is that if you take the first letter of each of these words and put it at the end, and then spell the word backwards, you wind up with the original word.

For example, voodoo is V-O-O-D-O-O, you put the V at the end and it's V-O-O, D-O-O backwards. OK? Now before we get 9,000 emails saying there are many more words you can add to this list, I know there are.

 

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The Jealous Neighbors
RAY: This week's Puzzler was sent to me from Bruce Robinson, a professor of civil and environmental engineering at the University of Tennessee. I think he sent it sometime in 1980, so he’s probably quit or retired by now!

There are 25 jealous people who live in the squares of a five-by-five grid. We're gonna number the squares, starting in the upper left-hand corner, 1 through 25.

The first row starts with 1, the second row starts with 6, the third row starts with 11, and so forth.

Remember, each person is jealous of his adjacent neighbor. Not his diagonal neighbor, but the person up or down or left or right of him. Each aspires to move into the apartment of his adjacent neighbor.

The question is very simple: What is the fewest number of total moves that can accomplish this?

 

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The Jealous Neighbors
RAY: This week's Puzzler was sent to me from Bruce Robinson, a professor of civil and environmental engineering at the University of Tennessee. I think he sent it sometime in 1980, so he’s probably quit or retired by now!

There are 25 jealous people who live in the squares of a five-by-five grid. We're gonna number the squares, starting in the upper left-hand corner, 1 through 25.

The first row starts with 1, the second row starts with 6, the third row starts with 11, and so forth.

Remember, each person is jealous of his adjacent neighbor. Not his diagonal neighbor, but the person up or down or left or right of him. Each aspires to move into the apartment of his adjacent neighbor.

The question is very simple: What is the fewest number of total moves that can accomplish this?

Answer:
RAY: So, if you draw this grid, the square in the upper left-hand corner we could say is one, and the one next to it is two, three, four, five, and then the line below that is six, seven, eight, nine, 10, 11, 12, right? All the way to 25.

Now, each person who lives on the floor aspires to move into the apartment of one of his adjacent neighbors. So number one can move to square number two, or number six, for example.

So, here's the question. Why would anyone live in such a stupid building? No, the question is, what is the fewest number of total moves that will allow every person to move to an adjacent square.

My first guess was that it had to be one, or zero. But my brother guessed “Millions of moves!”

And it turns out that he was right. Or at least, he was close!

If you don't number the squares 1 through 25, but instead, letter them, alternating A and B (so the first one is A, the next one B, the next one A, the next one B, et cetera, et cetera.) then, everyone who's on an A square must, by definition, move to a B square.

And everyone who's on a B square must move to an A square.

Now, if you add them up, by some stroke of bad luck, you’ve got 13 A squares and only 12 B squares.

Someone's got to move out of the building.

So there is no fewest number of moves. It is impossible for this to happen. I know, it was a little sneaky.

Impossible is a good answer.