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Car talk plaza puzzler revisited

Discussion in 'Gamers Zone' started by returntosender, Mar 1, 2021.

  1. Sabertooth

    Sabertooth Repartee Animal: Quipping the Saints! Supporter

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    Counting Hairs
    Let's say you have a town in which there are 200,000 people.

    I want to know, what are the chances that two inhabitants of that town will have exactly the same number of hairs on their heads? Now I will. I will stipulate that no one in this town can have more than 100,000 hairs and nobody will have fewer than zero.

    So you have a town of 200,000 people. And you have heads of hair that have between zero and 100,000 hairs. So I want to know what are the chances that there are two inhabitants of this town that have exactly the same number of hairs? Not necessarily in the same place. You could have like you want hairs on the front and somebody could have eight hairs on the back and that would be a match.
     
  2. Sabertooth

    Sabertooth Repartee Animal: Quipping the Saints! Supporter

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    100%
    (There are 200,000 people with only 100,001 "counts" available.)
     
  3. Sabertooth

    Sabertooth Repartee Animal: Quipping the Saints! Supporter

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    Answer:
    This is a branch of mathematics known as like common tutorial [sic¹] analysis. And this is a well known pigeonhole principle. You take the first 100,000 people and you distribute them such that no two people have the same number of hairs. You put each one of them on a little pigeonhole.

    You say, "Okay, how many hairs you got? Zero, Okay, you go in the zero pigeonhole."

    Next guy goes in "one" next person was in "two". So you've used up 100,000 [sic²] residents, and you've used up all 100,000 pigeonholes.

    So the very next person, the 100,001st² person is back where? They must be a duplicate of one of the first 100,000.

    So as a matter of fact, there are 100,000 people in this town that have the same numbers of hairs on their heads. They all have a mate (or many mates!)³

    I thought I'd share the reviews on this one. My brother said, "That is the most inane, great puzzler I've ever heard!"

    And Doug left a little note for me on this one: "Raymond, I never had time to tell you last week, but this is one of the most inane puzzles you come up with in a long time. Love, your inestimable producer, Douggie."

    ¹I think that he meant "combinatorial" analysis.
    ²Having a range from 0 to 100,000 grants 100,001 possibilities (0 counts as one). Person #100,002 would be a necessary duplicate.
    ³Not true. Some hair counts might belong to only one person or none, but there is no way for all hair counts to be used only once.
     
    Last edited: Oct 31, 2021
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  4. Sabertooth

    Sabertooth Repartee Animal: Quipping the Saints! Supporter

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    Of Streets and Surnames
    We're gonna make it a two-part puzzle. Part A is: what is the most common street name in the United States?

    By common, we mean "most used." So if you went to every single town, village, and hamlet or fair city in the United States and looked at all the street names and tallied up every street name that you found, number one on the list would be ___? And no it would not be Maple Street. So that's the first part.

    Part B, we know that the most common surname is Smith. But what is the second most common?
     
  5. Sabertooth

    Sabertooth Repartee Animal: Quipping the Saints! Supporter

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    (They changed their posting schedule.)
    You know what the most common street name is? This was surprising to me. "Park Street" is the most common street name. "Main Street", on this ranking of streets, is number 32. And that's shocking!

    And the second most common name is street name is "Washington Street."

    For the second part of our puzzler, the second most common surname is "Johnson". "Jones" is number 4!
     
  6. Sabertooth

    Sabertooth Repartee Animal: Quipping the Saints! Supporter

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    Number Sequence
    It's time for the new puzzler and this is this one is a good one. This is a very simple one. All of us are familiar with with the kinds of puzzles where we give a sequence of numbers and ask you to name the next term.

    For example, one, three, five, seven, nine, twenty-three. What's the next term? Right?

    Well, this is just like that. And I'm going to read it just like that. I'm going to give you a string of numbers all separated by commas. And I will say where the commas are. And I want you to give us the next term.

    Here's, here's the sequence of numbers. "1 comma 11 comma 21 comma 1211 comma 111,221 comma space." Now, what's the next term?

    Now to be fair, my brother insisted that I had given you the numbers wrong, so here's how he read them.

    "1 <pause> 11 <pause> 21 <pause> 1211 <pause> 111221 <end>"

    And neither one of those things will help you at all! My brother was adamant that we also ask you why? So our question is, what's the next term and why?
     
  7. Sabertooth

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    The next number is 312211.

    The key is that each number is telling you what the previous number was. So the first number is one. The second number says that the previous number was one, one. Get it?

    Right though the 11 means 11 is one, one. The next number two, one is telling you what the previous number was, what was the previous number 11? So this next number is two, one.

    It's just defining or numerating or whatever a number of digits.

    The next one after 21 would tell you that there's one two, and one one which is 1211.

    Then there was one one, one two, and two ones. Then there were three ones, two twos and one one.
     
  8. Sabertooth

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    Miss Pronunciation
    From time to time, I like to do a puzzle that's brief. I mean, you know, not one of these verbose puzzles that require lengthy explanations and dissertations. Sometimes I like to just keep it simple.

    Now this one is a two-part puzzler and it has to do with the English language.

    Part 1. I was listening to the radio the other day, and as luck would have it, I was listening to the BBC. And they keep mispronouncing this word and I thought I'd set the record straight.

    There's the stuff that beer cans and the like are made out of in this country, which the English consistently call al-u-mini-um. Yeah. And of course, as everyone knows, we call them tin cans. Or we call them beer cans or aluminum cans.

    So Why do they call them al-u-mini-um cans? Or why do they refer to that metal as al-u-mini-um?

    So the first part has to do with that material, why do they mispronounce it?

    And now for the highly technical, automotive part of the puzzle, part B:

    What does STP stand for? We're betting there are three people in the whole planet that know this!
     
  9. jacks

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    When I'm feeling prideful, I often come to this thread...instant humility! Even when I see the answers I can just barely get it!

    I do have a real Car Talk question, my dad and I called in and never got the correct answer.

    We had a Renault 16 (actually we had 3, it took that many to keep one running.) It's problem was that it would run ratty when ever we gave it a lot of gas on a hill. We had a very steep, rough driveway with lots of turns about 1/2 mile long. The car would run fine on the roads and freeway, but when we gave it a lot of gas to get up the hill, it would cut out badly. Often we couldn't get it up the hill and would leave it to the next day. It would then run just fine then. Things we had tried included new spark plug, wires, distributor, rebuilt carburetor, clean air filter and checked a variety of sensors, etc.
    We eventually found the answer by chance. If anyone wants to try the answer, you will have out done the Car Talk folks! I will post the answer in a day or two, in case anyone is interested.
    The misfire was caused by a loose manifold. When the car hit a bumpy, steep road, the manifold dropped down a bit and allowed exhaust to enter the carburetor. Who'd of thought!?
     
    Last edited: Nov 29, 2021
  10. Sabertooth

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    So many elements end in "-ium," like uranium & plutonium, that it has become force-of-habit over there.

    (I wonder if they mispronounce "platinum," too...)
     
  11. Sabertooth

    Sabertooth Repartee Animal: Quipping the Saints! Supporter

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    Answer:
    Remember last week's puzzler? I was listening to the BBC and I noticed that the British pronounce the word aluminum as al-u-min-i-um.

    And then I asked myself, "Who, pray, told you they mispronounce this word?" and then I thought maybe they aren't mispronouncing it. Maybe we mispronounce it, at least in their view.

    So I went and I looked at my Funk & Wagnall's dictionary. I actually tried to get Paul Murky of Murky research to look in this but he was busy doing some upholstery.

    So I looked it up. And it turns out that we spell it aluminum with no "i-u-m."

    But the reason they say "al-u-mini-um" is that that was the original spelling that in fact we used to use in this country up until 1925. It was spelled "aluminium". But those tin men couldn't sell aluminium siding. So they changed the word.

    Now here's Part B: What does STP stand for?

    My brother actually got this one right away, through the intervention of divine luck, and it's "Scientifically Treated Petroleum".
     
  12. Sabertooth

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    Not Being Facetious!
    I can see by that puzzled look on your faces that you know what time it is. Time for the new puzzler!

    I was reading the other day and I came across an interesting word. Now, this is no joke, I'm not being facetious. The word is "facetious".

    So there is something interesting about that word. And I can't tell you what it is. But if you write it down, you will notice that there is something interesting about it.

    To the best of my knowledge, there is only one other word in the English language that has the same properties.

    So this is again, a two-part puzzler column. Part 1: What is it that's peculiar, unique, or interesting about the word facetious? And Part B: What other English word has the same peculiarity?
     
  13. Sabertooth

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    It contains all five vowels, occurring in alphabetical order.

    "Facetiously" contains all six vowels in alphabetical order.
    Part B:
    There are many words that share the same quality as my Part A guess.
     
    Last edited: Nov 29, 2021
  14. Sabertooth

    Sabertooth Repartee Animal: Quipping the Saints! Supporter

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    Answer:
    Alright, it's time for [Ed. note: Ray pauses for trumpet fanfare] the new puzzler!

    Now last week, I asked you what was unique about the word "facetious" and the answer is this word has all of the vowels.

    Or at least what we commonly call vowels, not counting Y.

    So "facetious" has each one of the vowels once and once only, and they're in the order they appear in the alphabet, so alphabetical order.

    Once you figured out that that was the unique property of the word facetious, can you figure out the other word? That was Part B of the question.

    So the second word that I came up with was "abstemious"!

    I mean, I have a feeling that there have to be many more words because there are so many that ended i-o-u-s.

    So all you have to find is one with an "a" and an "e" in the right place. So the problem is having them only ever each letter each vowel only once. We'll see in the weeks to follow whether anyone comes up with a word beyond abstemious.
     
  15. Sabertooth

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    Coring the Sphere
    It's time for the new puzzler. I already presented this puzzle as a challenge to our staff here at Car Talk Plaza. And I'm going to use it because Doug Berman is still scratching his nose, trying to try to figure it out.

    I think the question has to be very carefully worded.

    You have a sphere, a solid sphere. And I don't want to tell you how big the sphere is because you have to figure that out. So you are going to drill through this to the center of this sphere with a tool, a drill. Or something like a drill, except the drill, is like a coring thing that you would core an apple with. A corer, if you will!

    You are going to take this corer, and make a hole through the center of a sphere.

    And the core is exactly six inches long. Or the corer is in fact a cylinder whose height is 6 inches.

    So you're gonna push this cylinder through the sphere. Imagine if you were coring, let's say orange. So you're gonna push this thing through until the piece falls out the other end. Both the corer and the piece fall out.

    Now the question is, how much of the material of the original sphere is left behind?

    Now you'll notice I didn't fool around with any semantics or jargon. And I didn't obfuscate the puzzler, because I was remonstrated by everyone here, including especially Doug was said, this puzzler was lousy, and that I should make it as clear, succinct, concise, uncomplicated, as possible.

    And the question is, how much of the sphere remains after you take out the 6" core?
     
  16. Sabertooth

    Sabertooth Repartee Animal: Quipping the Saints! Supporter

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    c = the length of the corer, 6"

    The puzzle left out the diameter of the corer, d.
    A nominal apple corer has a diameter of 0.75".
    The radius of the corer, r = d/2 = 0.375".

    The largest diameter* that this sphere can have (where the corer can breach its opposite side) is D,
    where D = √(c² + d²) = 6.047".

    The radius of the sphere, R = D/2 = 3.023".
    The original volume of the sphere, V = 4πR³/3 = 115.758in³.
    The approximate volume of material removed by the corer, C = cπr²
    = (6")π(0.141in²) = 2.651in³.

    The approximate leftover volume, v = V - C = 115.758in³ - 2.651in³ = 113.107in³.

    *A sphere with a smaller diameter can also be breached, but will have a different solution.
     
  17. Sabertooth

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    Answer:
    I have a semi answer to this puzzler that was the last one.

    My biggest disappointment was that Doug Berman got the answer right away. I thought it was a good puzzle.

    But if Doug gets the answer, then it's clear that was not a very challenging puzzle. Well, maybe I didn't stable may not realize that that you've heard of the organization called Mensa, which is for people with very, very high IQs. Well, Doug has just started an organization for automobile mechanics. He calls it Densa. He's the president.

    So my brother figured out the answer, not even understanding the question, because of what was missing from the answer. He said, "since you did not specify the size of the sphere, that it must not make any difference. Therefore, I can make the sphere be any size I want it to be. It's right. And I chose to make it 6" in diameter."

    Because we didn't specify what the diameter of the core was to be. We use limit theory. If it weren't for that, I would have no idea how to figure this out. Because if you use limit theory, and you shrink the diameter of the core down to zero, then the answer becomes four-thirds pi R cubed with R being three. And the answer becomes 36 pi units. Cubic inches, we said.

    Pi R cubed, and you make R be whatever the heck you want it to be. In this case, the limit theory says it ought to be three.
    ~~~~~~~~~~~~~​
    This answer did not make sense to me.
    If the corer has a fixed diameter, a different diameter sphere <6" would have a different percentage of material left behind.
     
  18. Sabertooth

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    What's That Sound?
    This is a non-mathematical puzzler. In fact, I'm not so sure what field of endeavor this comes in.

    So you're driving in your car and you drive by things like telephone poles. And you hear "Whuuh . . . . whuuh . . . whuuh!"

    And if my brother's driving, you hear, "Whuuh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . whuuh." Even that was probably too fast, for my brother's driving!

    Here's the question. What are you hearing? When you drive by a telephone pole or some other regularly or irregularly spaced things on the side.

    You hear this noise. What is it?
     
  19. Sabertooth

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    Answer:
    Most of the incorrect answers that we got suggested that what you're hearing is air rushing past the tree. Absolutely wrong!

    Because if you look at it in the Einsteinian framework of things, frame of reference, the trees ain't moving. And so if you were standing next to one of those trees, would you hear that noise?

    And the answer is no, you would not hear that if you were standing next to one of those trees.

    Do you know what you would hear? You'd hear the car going by here. And that's what you hear. When you go by the tree, you hear the noise that your own car is making, bouncing off the tree. So what you hear is the engine, exhaust, the noise of the tires on the road, the wheel bearings, the transmission that is grinding itself into all those little pieces.

    For a split second, that sound is bouncing off the utility pole, and that's what you hear.
     
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