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Post by Dizzy D on Feb 10, 2017 8:31:17 GMT -5
Another math riddle, with a comic twist this time.
Professor X asks his two best students to the front of the class. Kitty and Doug appear and Xavier asks them both to think of a whole, positive number between 0 and 100. They both do.
Xavier then goes to the blackboard and writes down two numbers on it: 54 and 73. He tells them that 1 of these numbers is the sum of both their numbers.
He asks Doug if he knows what Kitty's number is. Doug replies: "No."
He then asks Kitty if she knows what Doug's number is. Kitty also replies: "No."
Xavier gives them a few minutes to think about it.
He asks Doug again, but Doug still does not know.
He then asks Kitty and Kitty replies that she knows that Doug's number is 21.
How did she figure it out?
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Post by berkley on Feb 11, 2017 19:19:28 GMT -5
I think I have this one figured out: Professor X Asks Doug if he knows Kitty's number. He knows his own number is 21, so Kitty's must be either (54 - 21) = 33 or (73 - 21) = 52, but he can't tell which.
Let's take 52 as Kitty's number (you have to check both possibilities, but I'll skip the one that led nowhere).
Prof X asks Kitty if she knows Doug's number. She thinks, it has to be either (54 - 52) = 2 or (73 - 52) = 21, but can't tell which.
Prof X comes back to Doug with the same question, and he still can't tell which of the two possibilities Kitty's number might be.
Prof X asks Kitty her question again, but this time she has another piece of info: she knows that Doug was unable to answer his question the second time even though he too had an extra piece of info, the fact that Kitty couldn't answer her question the first time around.
So Kitty reasons that:
Doug's number is either 2 or 21.
if Doug's number was 2, then the second time he was asked the question he would have thought:
Kitty's number can be either (54 - 2) = 52 or (71 - 2) = 71.
But if her number was 71, then the first time she was asked, she would have reasoned:
Doug's number is either (54 - 71) = -17, or (73 - 71) = 2
Therefore, Doug's number is 2, the only positive number of the two possible solutions.
So if Kitty's number is 71, she would have known that my (Doug's) number must be 2 and would have answered the question the first time.
She couldn't answer, therefore her number is 52
so if his own number was 2 Doug would have been able to answer the question the second time he was asked.
But Doug wasn't able to answer the question, therefore his number is not 2, but 21.
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Post by Dizzy D on Feb 13, 2017 2:37:48 GMT -5
That's basically it, they can infer a bit more information per step:
Step 1: The first time Doug answers no, Kitty knows that Doug's number must be less than 54, otherwise, there would have been no reason for him not to directly know the right answer. So Doug's number is more than 0 and less than 54.
Step 2: The first time Kitty answers no, Doug knows that like his number, Kitty's must be less than 54 (for the same reason as he didn't know), but also more than 19 (the difference between 88 and 73), because if her number was less than that, 88 would not have been a possibility (as Doug's number must be less than 54 as they realised in step 1).
So Kitty's number is more 19 and less than 54.
Step 3: Even knowing that Kitty's number must be more than 19, Doug can't answer, so Doug's number must be less than 35 (54-19), otherwise he would have known the answer because if his number is higher than 54 can no longer be a valid sum.
From that point in each step just narrows down the range of the numbers, raising either the lower limit (for Kitty's number) or lowering the top limit (for Doug's number) by 19 for each step.
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Post by Rob Allen on Feb 14, 2017 23:34:24 GMT -5
RAY: This puzzler was sent in by Bill Kojuck, who writes: Last year, a friend of mine and his wife went on vacation to Key West. They spent most of their time either sport fishing on the high seas or carousing on Duval Street. My wife and I, however, prefer a very different kind of vacation. We like hiking and camping and using stone-age toilet facilities. So, we spent most of our vacation in the woods in California and the Pacific Northwest. When we returned from our trips, we compared notes. I said to my friend that on our vacation we saw something that, when written down, has all five vowels -- and the vowels make up five of the seven letters in the word. TOM: You mean, A-E-I-O-and-U were all in the same seven-letter word? RAY: Right. Bill goes on: In fact, we saw not just one, but a few of these things. My friend said, 'When we got to Key West, we also saw something that when written down has all five vowels in its seven letters. In fact, we saw quite a few of these as well.” Each of us wrote down our seven-letter word, and then exchanged papers. They were the same word. But what I saw and what he saw were very different things. The question is, what did each of us see? The answer: RAY: What he saw was some rather large sport utility vehicles called Sequoias. And what we saw - TOM: Were trees. RAY: Right. We saw some very large trees called sequoias. And the next puzzler: RAY: About 40 years ago, a guy took a job as a traveling salesman. He immediately fell out of favor with his boss, who assigned him to spend the winter traveling around exotic places like Moose Jaw, Maine and Freeze-Your-Butt, New Hampshire. He had to travel by car from one location to another, so he often found himself driving from town to town in the winter looking for cheap motels in which to spend the night. He began to notice a disturbing thing. When he would stop at these motels, oftentimes the owner of the motel was also the clerk, and they'd have you fill out that little card--you know, name, address, home phone--in case you skipped out in the middle of the night. Also, the motel owner would ask him what he did for a living. When he said he was a salesman, he would almost always be assigned a room on the second floor. I asked him if it had anything to do with the car that he drove. And he said, "I guess you could say so. At the time I was driving a Volkswagen." And that's your hint. Why was he always assigned to a room on the second floor? |
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Post by Rob Allen on Feb 20, 2017 19:10:51 GMT -5
RAY: About 40 years ago, a guy took a job as a traveling salesman. He immediately fell out of favor with his boss, who assigned him to spend the winter traveling around exotic places like Moose Jaw, Maine and Freeze-Your-Butt, New Hampshire. He had to travel by car from one location to another, so he often found himself driving from town to town in the winter looking for cheap motels in which to spend the night. He began to notice a disturbing thing. When he would stop at these motels, oftentimes the owner of the motel was also the clerk, and they'd have you fill out that little card--you know, name, address, home phone--in case you skipped out in the middle of the night. Also, the motel owner would ask him what he did for a living. When he said he was a salesman, he would almost always be assigned a room on the second floor. I asked him if it had anything to do with the car that he drove. And he said, "I guess you could say so. At the time I was driving a Volkswagen." And that's your hint. Why was he always assigned to a room on the second floor? And the answer is... RAY: Here were the hints: He started working 40 years ago. He drives a lot, he's concerned about getting what? Good mileage. So he buys himself a Volkswagen. But not just any old Volkswagen. A VW diesel. Because he's in Moose Jaw, Maine, and Freeze-Your-Butt, New Hampshire, in the wintertime, he's got to plug the thing in overnight. Otherwise, it won't start. The reason the motel owners put him on the second floor all the time is so they could see the extension cord that the salesman had run from his motel room to his car. Being annoyed at the salesman's petty electrical theft, the motel owners would unplug the extension cord in the middle of the night. And another new Puzzler: RAY: Long, long ago when he was just a lad, our producer, Dougie Berman, had three girlfriends. On Monday he would visit one, on Tuesday another, on Wednesday, the third one, and then he would repeat the process. On Thursday he would visit number one, etc. And each time he would make one of these visits, he would drive his car, but before he could drive the car, because it was a junker, he had to go through a little ritual. He would open the hood, and he would have to top off the coolant because it leaked coolant. He had to top off the power steering fluid. That leaked too. He had to fill up the oil because it was burning oil like crazy. So he closes the hood, drives to girlfriend number one's house, and follows the same procedure every time he pulls into the driveway, and then he drives as far into the woods as he can so the other girlfriends won't see his jalopy. He does this for girlfriend number one, and then on Tuesday for girlfriend number two, and on Wednesday girlfriend number three, but when he pulls into girlfriend number three's driveway, an interesting thing happens. Fire erupts under the hood. The thing bursts into flames. At which point, he jumps out of the car, removes his pants, and beats out the flames. Then when the thing has finally subsided, he stashes the car, goes to her house, and tries to explain to her parents why he is coming to meet her with no pants on. So this goes on and on, girlfriend number one, no problem, number two, no problem. But every time he visits girlfriend number three, same problem, the car catches fire under the hood. He can't explain it. He takes this as an omen and dumps the other two girlfriends, and keeps girlfriend number three, because any girl that can set his pants on fire has got to be worth sticking around for. So what is it about his visit to girlfriend number three that causes this conflagration under the hood? |
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Post by Rob Allen on Feb 27, 2017 13:25:21 GMT -5
RAY: Long, long ago when he was just a lad, our producer, Dougie Berman, had three girlfriends. On Monday he would visit one, on Tuesday another, on Wednesday, the third one, and then he would repeat the process. On Thursday he would visit number one, etc. And each time he would make one of these visits, he would drive his car, but before he could drive the car, because it was a junker, he had to go through a little ritual. He would open the hood, and he would have to top off the coolant because it leaked coolant. He had to top off the power steering fluid. That leaked too. He had to fill up the oil because it was burning oil like crazy. So he closes the hood, drives to girlfriend number one's house, and follows the same procedure every time he pulls into the driveway, and then he drives as far into the woods as he can so the other girlfriends won't see his jalopy. He does this for girlfriend number one, and then on Tuesday for girlfriend number two, and on Wednesday girlfriend number three, but when he pulls into girlfriend number three's driveway, an interesting thing happens. Fire erupts under the hood. The thing bursts into flames. At which point, he jumps out of the car, removes his pants, and beats out the flames. Then when the thing has finally subsided, he stashes the car, goes to her house, and tries to explain to her parents why he is coming to meet her with no pants on. So this goes on and on, girlfriend number one, no problem, number two, no problem. But every time he visits girlfriend number three, same problem, the car catches fire under the hood. He can't explain it. He takes this as an omen and dumps the other two girlfriends, and keeps girlfriend number three, because any girl that can set his pants on fire has got to be worth sticking around for. So what is it about his visit to girlfriend number three that causes this conflagration under the hood? The answer is... RAY: What is it about his visit to girlfriend number three that causes this conflagration under the hood and ultimately... in his pants? TOM: Does it have something to do with power steering fluid and the shape of the driveway? RAY: Exactly. I mentioned earlier in the story that he added coolant; he was leaking coolant. He was adding oil, but he's burning oil. TOM: He’s burning the oil. The coolant is not going to extinguish the flame. RAY: He adds power steering fluid. When he pulls into the driveway of girlfriend number three, he has to make a very sharp turn. He has a leak in the high pressure power steering hose, and when this wheel is cut all the way, the increased pressure of the system squirts it out onto the hot exhaust manifold, and that small amount of fluid -- vroomm! -- bursts into flames. TOM: Wow! And the new Puzzler for this week: RAY: A rich old geezer passes away. When the lawyer reads the will, he's surprised to find out that the old geezer left his entire estate to his three nephews, Chip, Skip and Nunzio. But the old man had the good sense to spend most of his money on women and wine. The only thing he had left was 17 sports cars. So the lawyer and the three legatees -- Chip, Skip and Nunzio -- show up at the carriage house to look at the cars. The lawyer says, "Your uncle left one-third of the cars to Chip, half of the cars to Skip, and a ninth of the cars to Nunzio." Chip, Skip and Nunzio look at each other and say, "What the heck do we do now? There are 17 cars." They don't know how to divvy them up. The lawyer's no help. They're ready to duke it out when who should waltz in but our old friend Crusty. Crusty proposes a solution. What did he propose and, more importantly, why did it work? |
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Post by Rob Allen on Feb 27, 2017 13:29:46 GMT -5
I can't think of anything except selling all the cars and splitting up the money. I'm not sure if the fact that one-half plus one-third plus one-ninth doesn't add up to 1 makes a difference.
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Post by berkley on Feb 27, 2017 19:09:48 GMT -5
How about they pretend there were 18 cars for purposes of easy, whole number division, so Chip gets 6 cars, Skip gets 9 cars, and Nunzio gets 2 cars, That adds up to 17, so they just ignore the 18th car, which doesn't exist anyway?
(edit: this can't really be the answer, can it?)
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Post by Dizzy D on Feb 28, 2017 10:07:47 GMT -5
These car riddles always seem to based on missing information we do not get, so I bet there is some car out there which we didn't hear about (he had a horse and carriage, a motorbike or something), so we get to 18.
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Post by Rob Allen on Feb 28, 2017 11:25:52 GMT -5
How about they pretend there were 18 cars for purposes of easy, whole number division, so Chip gets 6 cars, Skip gets 9 cars, and Nunzio gets 2 cars, That adds up to 17, so they just ignore the 18th car, which doesn't exist anyway? (edit: this can't really be the answer, can it?) Yes, it can be and I think it probably is the answer. |
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Post by berkley on Feb 28, 2017 19:40:32 GMT -5
Yeah, I don't really get these car questions either - including this last one.
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Post by Rob Allen on Mar 6, 2017 19:16:22 GMT -5
RAY: A rich old geezer passes away. When the lawyer reads the will, he's surprised to find out that the old geezer left his entire estate to his three nephews, Chip, Skip and Nunzio. But the old man had the good sense to spend most of his money on women and wine. The only thing he had left was 17 sports cars. So the lawyer and the three legatees -- Chip, Skip and Nunzio -- show up at the carriage house to look at the cars. The lawyer says, "Your uncle left one-third of the cars to Chip, half of the cars to Skip, and a ninth of the cars to Nunzio." Chip, Skip and Nunzio look at each other and say, "What the heck do we do now? There are 17 cars." They don't know how to divvy them up. The lawyer's no help. They're ready to duke it out when who should waltz in but our old friend Crusty. Crusty proposes a solution. What did he propose and, more importantly, why did it work? Here's the rather familiar-looking answer, with one extra twist: RAY: Here's the answer. The first nephew Chip inherited a third of the 17 cars. Skip, the second guy, is going to get half the cars. And Nunzio is going to get one-ninth of the cars. So Crusty comes along and says, 'Look guys, I'll lend you my '52 Studebaker so now you can divide up 18 cars.' So Skip says great, 'I'll take half of the cars, or nine cars.' Chip says, 'I'll take a third, that's six cars.' And Nunzio says, 'I'll take one-ninth or two cars.' Now if you add those up it's 17 cars. So Crusty gets his '52 Studebaker back and everything's done and everyone's happy. The reason it works is that half plus a third plus a ninth do not add up to one. The old geezer originally had 18 cars. But because they don't add up to one, in fact when each gets his nine or six or two cars, it's actually more than the old man wanted to give each in his will. Congrats to berkley for figuring it out! The question for this week, a non-car-related question, is: RAY: A teacher named Ms. Jones asks her third grade class if it's anyone's birthday that day and, to her surprise, even though there are 30-something kids in the class, no one raises their hand. Ms. Jones then asks, "Well, is there anyone here who has a family member whose birthday it is today?" And little Katie raises her hand and says, "As a matter of fact, today is my father's birthday, and it's also my grandfather's birthday." The teacher says, "Oh really -- how interesting!" Little Katie goes on to say, "And they're the same age." The teacher says, "Oh, no, no, Katie, that can't be." But Katie insists that they’re the same age. So the question is: Can it be and, if so, how? Now, if you start thinking about February 28th and all that, you're barking up the wrong tree. |
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Post by Deleted on Mar 15, 2017 12:46:36 GMT -5
He's the product of incest.
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Post by Rob Allen on Mar 15, 2017 14:01:11 GMT -5
No, Katie's mother married a man who's the same age as her father.
Official answer soon - they've revamped their website and it wouldn't come up yesterday.
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Post by Rob Allen on May 11, 2017 17:04:22 GMT -5
RAY: A teacher named Ms. Jones asks her third grade class if it's anyone's birthday that day and, to her surprise, even though there are 30-something kids in the class, no one raises their hand. Ms. Jones then asks, "Well, is there anyone here who has a family member whose birthday it is today?" And little Katie raises her hand and says, "As a matter of fact, today is my father's birthday, and it's also my grandfather's birthday." The teacher says, "Oh really -- how interesting!" Little Katie goes on to say, "And they're the same age." The teacher says, "Oh, no, no, Katie, that can't be." But Katie insists that they’re the same age. So the question is: Can it be and, if so, how? Now, if you start thinking about February 28th and all that, you're barking up the wrong tree. Well, life got in the way of posting the answer to this, but here it finally is: RAY: They're the same age because her father and her grandfather are not related. Her father is an old geezer who married some young woman whose father is the same age as he is. There have been several Puzzlers in the intervening weeks, which I'll post if there's interest. Here's the current one: RAY: I'm going to give you a thousand $1 bills. You come up with 10 envelopes. Here's your assignment: Figure out a way to configure those 10 envelopes, that is, to put various numbers of dollar bills in those 10 envelopes, so that no matter what amount of money I ask you for, you can hand me some combination of envelopes and always be assured of giving me the correct amount of cash. TOM: Let me get this straight. If you say, "Give me $637," I can say, "Oh, that will be envelope number one, envelope number six, and envelope number two." RAY: You got it. |
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