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Post by Deleted on Nov 10, 2017 20:33:14 GMT -5
A local billboard in my area reads: An Atheist belongs to an Non-Prophet Organization
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Post by Prince Hal on Nov 11, 2017 10:45:26 GMT -5
The somewhat-belated answer is: RAY: You could write an algebraic expression to answer this puzzler. For example, if you let X represent the amount of money that he started with, then after the first day he is left with X minus one, that quantity over two minus one. And then that just tells you how much money he's left with. Then you can run an expression, how much he has after the second day. And the third day, and set that expression equal to zero and solve. Or you could think about it backwards. If you wound up with zero then the last day he entered the casino he had to have walked in with three dollars in his pocket. So if on day three he had three dollars, then he had to have started the day before with nine dollars. And if you work backwards to the first day, he started with 21 bucks, and that's the answer. He had 21-dollars, paid a dollar to get in, he had 20 left, lost half of it. And so on. And the new challenge: RAY: This was sent in by Tom Ireland and I had to mess around with it a little. He writes: Where I live there are quite a few hills, many of them very steep. Some of them are quite a challenge for any vehicle, even those that are high performance. In fact, a few of these hills are so steep that I often have to ride up the whole way in low gear, especially if I happen to catch a red light at the bottom like I did the other day. A few days ago I found myself going not up one of these hills, but down a long steep grade. I found myself gaining speed at an alarming rate. Shifting even into the lowest gear didn't help at all and I had to apply my brakes almost the entire way down to keep from going so fast that I'd lose control and crash. The brakes got really, really hot, but I was able to stop safely at the red light at the bottom of the hill. Here's the interesting part: There's nothing wrong with my vehicle. It's in perfect working order. So the question is, why did I have to use my brakes to maintain a safe speed going down that hill? And why, despite the fact that I put it in first gear, did it not slow me down in the slightest? My guess is that he's riding a bike. Not enough weight to slow down the momentum. In a car, it's the weight of the vehicle that's helping to slow you down. Not even close to the same weight with a bicyclist and a bike. |
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Post by Rob Allen on Nov 13, 2017 19:32:14 GMT -5
Prince Hal wins the Puzzler no-prize this week!
The official word(s):
RAY: I thought I did an admirable job of obfuscating this. Here's the answer: When you shift your car into low gear, you are using the inertia - the mass of the engine to slow the car down. So when you're in first gear for example, you are asking gravity to pull the car down the hill, and you're asking that gravity to turn the pistons and the crankshaft and all of that stuff. And that's more likely to slow the car down, better than being in second, or third or fourth gear.
TOM: Yeah.
RAY: However, that will not work with all vehicles. Like bicycles. So if you are riding a bicycle, it makes no difference what gear you're in going down the hill because there are no pistons or crankshaft. You are the engine and you are coasting and the only thing that can slow you down going down the hill --
TOM: Is the brakes.
RAY: Or a tree! A tree works really well.
Personally, I don't recommend the tree option. Anyway, on to the new challenge:
RAY: This is from my delivery truck series and it was sent in by Rob Gretigney.
He writes:
I once worked as a delivery truck driver. The truck I drove was about 25 feet in length. One of the places that I routinely delivered to required that I pull into a narrow alley in order to unload my truck. One cold January day after making my delivery I discovered that my battery was as dead as a hammer. I had probably left my lights on when I went for coffee.
Another delivery driver had pulled into the alley right behind me and I asked if he had a set of jumper cables and a strong battery that I could use. He did but the jumper cables were only 16-feet long and wouldn't reach from his battery to mine. The alley was too narrow to park the truck with the good battery next to mine, and my truck was too heavy to be pushed into a better position. We did think about temporarily replacing my battery with the one from the other truck so that we could at least get out of the alley, but the cable connections were so corroded on both vehicles that they wouldn't budge. And, to top it off, we didn't have any tools anyway.
Then I struck upon an idea that allowed us to get my truck started in only a few short minutes. What was the idea?
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Crimebuster
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Post by Crimebuster on Nov 13, 2017 20:38:19 GMT -5
This may be too obvious, but couldn't the second truck just back out, drive around, and enter the alley from the other side so the trucks are parked nose to nose?
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Post by Rob Allen on Nov 20, 2017 18:22:23 GMT -5
Apparently this was an alley with only one entrance. The official answer:
TOM: I know the answer! You put the two cables together and you put the bumpers touching.
RAY: Exactly. Jumper cables consist of two wires with clamps on each end so you've got four clamps. They're kind of stuck together through the insulation, and if you peel them apart and then clamp the ends together, you have instead of one 16-foot long pair of jumper cables, you have one 32-foot long cable, but you only have one. But trucks have steel bumpers and steel frames, and the steel of the frame is the conductive path for all the electrons.
TOM: Phew.
RAY: You've made the electrons travel through one cable, and then through the frames of both vehicles to get back to the original jumping battery, and voila -- the thing was started.
And the new Puzzler asks us to do some arithmetic:
RAY: This was sent in by John Kelly and he writes with a true story:
"While living in the Bronx a friend, who will remain anonymous, bought a car in White Plains about 21 miles north of the city. He didn't have anyone to help him pick it up so he decided to do it all by himself." (Now whenever someone says, "a friend who will remain anonymous," and then the rest of the story is something harebrained, you know it's him! So John, we're with you, brother!)
"And because he wasn't trading the car in, he came up with this ingenious plan. He drove his old car 21 miles north and parked it in the dealer's lot, picked up the new car, paid for it and got the keys, and drove it one mile south. He locked it up, walked back north one mile to the dealer, picked up his old car drove it two miles. He locked it up, walked back one mile, picked up the new car, drove it two miles south, locked it up, walked one mile back to the other car, etc., etc., etc., until he reached home with both cars."
So the question is, at the end of the very long, long day, how many total miles did he walk and drive? Sounds simple, right, but be careful!
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Roquefort Raider
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Post by Roquefort Raider on Nov 20, 2017 18:46:57 GMT -5
I get 63 miles, but that’s from a back lf the envelope cartoon, not a proper calculation.
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Post by Dizzy D on Nov 20, 2017 20:15:28 GMT -5
63 miles driven that day (21 on the trip towards the dealer, then both cars are moved 21 miles home), 20 miles walked (he doesn't need to walk the last mile back), but it's late so I may miscalculate
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Post by Rob Allen on Nov 27, 2017 18:01:43 GMT -5
I think he did have to walk the last mile - he arrived home in one car, then walked back to get the other one. Here's what Ray says:
"RAY: Here's the answer. He clearly walked 21 miles, right? It would be the equivalent if he had driven up there with his old car and driven the new car home and then walked back up there. He just did it one mile increments. So he walked 21 miles, and he drove the new car back 21 miles.
TOM: Yeah.
RAY: So most people say, that's 63 total miles. Wrong! Everyone forgets the 21 miles he drove to get up there.
So he drove 21 miles to get to the dealership. And then drove two cars back --
TOM: 21 miles each.
RAY: Which is another 42 miles. Add that to the original 21 he drove up there the first time, 63 miles, and the and then the 21 that he walked, 84 miles, no wonder it took him all day. What was he, crazy?
And this week we have a seemingly impossible task:
"RAY: I stole this puzzler from a little book by Terry Stickles, and there's a foreword in here by Will Shortz, who, of course, is the puzzle editor of the New York Times and a frequent visitor to National Public Radio.
You've been invited to go on a camping trip in the woods with 30 of your closest buddies, and you've rented a cabin in the woods. You pile into your cars and drive to the cabin. The next morning, everyone gets up and decides that Cookie is going to make homemade pancakes for everyone, but he needs to add to the recipe exactly two gallons of water. So you are sent to the well to fetch two gallons of water with no measuring device. When you get to the well, you discover there are two jugs there. One says 13 gallons, and the other says seven gallons. And your job, if you choose to accept it, is to come back with exactly two gallons of water.
TOM: Can you make two trips to the well?
RAY: No, you can't! They're earthenware jugs! They're very heavy, and you've got a bad ticker, a bad back and a bad front. So you're allowed one trip. You got it?
TOM: Yeah, I got it."
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Post by Jeddak on Nov 27, 2017 19:01:28 GMT -5
Fill the small jug and pour it into the large one. Repeat; twice 7 is 14, so you'll be left with one gallon in the small jug. Empty the large jug. Pour the one gallon into the large one. Fill the small one and pour it into the large one, giving you 8 gallons in it. Repeat; this time the large jug will only take 5 more gallons (8+5=13). That leaves you with 2 gallons in the small jug. Now go eat. And have seconds; you deserve it after your 'friends' make you do the fetching.
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Post by Rob Allen on Nov 27, 2017 20:00:57 GMT -5
I came up with another way but yours is much simpler.
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Post by Jeddak on Nov 28, 2017 17:57:11 GMT -5
I tend to take the long way around on these things myself. At first, I thought the specific number of guests was significant. (31 seemed like a lot of people, eh?) But then I decided I was overthinking it, and focused on the jugs.
What was your solution?
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Post by Rob Allen on Nov 28, 2017 20:47:32 GMT -5
The long way:
Fill the large one. Fill the small one from the large one and discard the contents of the small one. This leaves 6 gallons in the large one.
Pour the six gallons into the small one. Fill the large one again, and fill the small one from it. There's only room for one gallon, leaving 12 in the large one.
Empty the small one and fill it from the large one. That leaves five gallons in the large one.
Empty the small one and pour in the five gallons. Fill the large one and fill the small one from it. There's room for two gallons, leaving 11 in the large one.
Empty the small one and fill it from the large one. That leaves four gallons in the large one.
Empty the small one and pour in the four gallons. Fill the large one and fill the small one from it. There's room for three gallons, leaving 10 in the large one.
Empty the small one and fill it from the large one. That leaves three gallons in the large one.
Empty the small one and pour in the three gallons. Fill the large one and fill the small one from it. There's room for four gallons, leaving nine in the large one.
Empty the small one and fill it from the large one. That leaves the desired two gallons in the large one.
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Post by Rob Allen on Dec 4, 2017 13:16:32 GMT -5
As expected, Ray's answer follows outsider's method:
RAY: Here's how you would do it. You take the seven-gallon container and you fill it up and you pour the contents of it into the 13-gallon jug. And then you do that again. And when you do that…
TOM: It's not all going to fit.
RAY: It's not all going to fit. You'll have filled the 13-gallon container, and you will have one gallon left over in the seven-gallon container.
TOM: Right.
RAY: You put that aside. You pour out the 13-gallon container. So now you have one gallon in the seven-gallon container, and the 13-gallon container is empty. You then take that one gallon and you pour it into the 13-gallon container, leaving room for 12 more gallons. You then fill the seven-gallon container again and pour the entire seven gallons into the 13 gallon container.
TOM: Now you're up to eight in there.
RAY: Now you're up to eight gallons, and you say, "Mmm. Eight. Room for how many more?"
TOM: Five.
RAY: Five. You then fill the seven-gallon container and you pour all but two gallons in, because there's only room for five in the 13-gallon container.
TOM: And you'll have two gallons left.
RAY: You'll have two gallons left, and if you don't trip and fall on the way back to the cabin, they'll be able to make the pancakes.
And this week's challenge:
RAY: We have a friend, Tommy and I, who shall remain nameless, who works at a government facility and does very, very important work.
TOM: Yes.
RAY: And one day, he's at his desk working away, reading some very technical manual when he's awakened … I mean, startled by the sound of his stomach growling. He turns in his seat and looks at the electric clock on the wall behind him. This is one of these clocks that's been there for, like, a thousand years. It plugs into the wall.
TOM: Big analog round thing.
RAY: Right. He looks at the clock, and as he turns back to his work, he says, "Well, it's obviously too early to eat lunch. I must have forgotten to eat breakfast." He begins to work. A short time later, he's again awakened, startled, by the growling of his stomach. And this time, he turns to look at the clock another time. You with me so far?
TOM: Yeah.
RAY: He looks at the clock another time, and he notices that it first of all says a time later than what it did the first time he looked at it. The second hand is sweeping. The hour hand has moved from where it was the last time he looked at it, and the minute hand is in a different position.
TOM: Mmm-hmm.
RAY: And as he turns back to his desk, again thinking that he must have forgotten to eat breakfast and he doesn't know how he's going to make it to lunchtime, his stomach growls a third time, and he says, "The clock is broken." And yet, everything seemed to be working.
TOM: Yeah.
RAY: Now, I may have to give a hint. The question is: How did he know the clock was broken?
TOM: Well, the minute hand, the second hand and the hour hand have all moved, you said.
RAY: Yeah. The two hands are exactly 180 degrees apart, like they would be at 6:00. That's the hint I was going to give.
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Post by Rob Allen on Dec 14, 2017 13:15:54 GMT -5
Nobody had an answer for this one, and Tom Magliozzi didn't like it much either:
RAY: Let's say he looked at the clock and he saw that the hands were 180 degrees apart, but the clock read 11:25. But it's impossible for it to be 11:25 and the hands be 180 degrees apart. Because when it's 11:25, in fact, the hour hand's...
TOM: It'd be beyond 11.
RAY: It should be 5/12 of the way to 12. He knew the clock was broken because it read a time that was impossible.
TOM: Oh, man! You are going to get so much hate mail for this one!
This week we have a calculation question:
RAY: This is stolen somewhat from an e-mail I got a long time ago. Here we go. Our erstwhile companion and chief mechanic, Vinnie Goombatz, being renowned for his prowess in arm wrestling, is asked to set up a tournament at the local watering hole where he goes and gets stewed every night. It's to be a single elimination tournament, i.e., once you lose, you're out. No ties allowed. This is arm wrestling; you can't have a tie in arm wrestling, right?
TOM: Yeah.
RAY: To his horror, 247 people have signed up for this tournament, and the barkeeper wants to know how many bouts have to be fought. Figuring a bout takes about five minutes, he wants to know at what time he should start the event so that it will conclude before closing time.
So Vinnie is in a tizzy now, because he's thinking about, Oh, I gotta set up a branching tree, count all the branches, and since he can't count much beyond 14, he's in a tizzy.
Fortunately, there's a little guy sitting next to Vinnie at the bar, and the guy says, "I know the answer." Vinnie says, "What are you, some kind of genius or sump'm?" The guy says, "No, but there is a simple reasoning process which will allow you to instantly know how many bouts have to be fought."
The question is: If there are 247 people that signed up, how many bouts will there have to be in order to determine one winner?
TOM: With a single-round elimination.
RAY: And show your work. And, by the way when the bout starts, both hands of the clock are 180 degrees apart.
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Post by Rob Allen on Dec 18, 2017 11:49:24 GMT -5
I think that line about the hands of the clock was just a reference to last week's Puzzler. It doesn't seem to figure in to the answer:
RAY: The question is, how many bouts have to be fought in order to determine one winner? One winner. So, you start off with 247 people. Divide that group in half, right? Half of them are gonna wrestle the other half. Then you're gonna lose half of those people.
TOM: Right.
RAY: And that half is gonna wrestle, right? You could go and do all this, but there's a simpler way to figure it out.
TOM: There is?
RAY: According to John LaTorre, who sent this to us, he claims that Albert Einstein used this as an example of elegant reasoning. That is, reaching a conclusion in the fewest number of steps in his math lectures. And here's the answer. Since you can't have any ties, every bout must have a winner and a loser. And since the thing is a single-elimination, everyone will lose once, and only once, except for whom?
TOM: One guy! The winner.
RAY: Therefore, how many losers are we gonna have?
TOM: Two hundred and forty-six.
RAY: How many matches are we gonna have?
TOM: Two hundred and forty-six.
And this week we have a car question:
RAY: This puzzler was submitted by Shelly Payne. Here it is:
Several years ago my father-in-law, who lives in Minnesota had trouble with his late model Cadillac DeVille. His battery kept dying every couple of days. He would get it jump started and it would run fine for a few days, but then would die again. So he took it to the dealership. They checked it out. They couldn't find anything wrong.
One morning after there had been several inches of snow he went out and sure enough, what? The battery was dead. So he jump started it and went into town to get a cup of coffee at the local drug store. Now being that he lives in such a small town, he went and parked right in front of the drug store. And while he was drinking his coffee, he complained to the pharmacist about how his car was driving him nuts. The pharmacist asked, "Is that your car right out there?"
And he said, "Why, yes, that is my car." And the pharmacist said, "I know why your battery is dying."
What did the pharmacist notice?
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