Einstein's Riddle (A Challenging Logic Puzzle)
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Took about 5 minutes with pen and paper. In fairness, I've solved this one about 20 years ago on napkins in the lunch room at school. Another fun "riddle" I remember from back then - albeit a much simpler one - is this one: A mathematics student in financial trouble sent a telegram to his (wealthy) father asking for money. Not having enough cash to send a long telegram, and knowing his father would appreciate a mathematical riddle, he sent the following: Dad, SEND + MORE =MONEY Thanks! How much did he need? To my knowledge there is only one logically sound solution to this. After solving it I made a pascal routine to solve it, and came up with a number (I seem to remember 24) of alternative solutions. Common to all of them was that they were somewhat logically flawed, although mathematically correct. //L
If your pascal routine delivered flawed solutions then it wasn't mathematically correct. ;) 1085 (presuming you meant to ask how much more he did need :cool: )
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I solved it with pure logic and pencil and paper in 20 mins. As a logic puzzle, it's fine. As presented with all the trimmings, there are some problems. Einstein didn't write this as a boy as shown, because Pall Malls had not been created yet. How much of the background story is true is very debateable. There are many versions of this floating around, and no evidence that I know of that Einstein actually created it. Nor do we know what he meant by saying only 2% of the population could solve it, if he even did say that. If the puzzle as written was not his, then what was it? If he wrote it, it was at least slightly different - and it might have been more difficult. Maybe people had less practice doing logic back then (indeed, they probably were less educated in general.) Maybe he meant doing it in your head with no pencil/paper. Who knows. I really doubt that as much as 98% of the population could not solve it. Was he counting relatively educated Western civilization only, or the entire world population? Starting at what age? Who knows.
The 'back then' argument sounds pretty convincing: nowadays every computer scientist knows the basics of logic reasoning, and most of them should be able to solve the riddle within at most a day. In Einstein's days, there was much less need to teach logic, and thus much less people familiar with techniques that are useful to solve these kind of riddles. I could easily believe that in the early 20th century only 2% of the world population could solve that. But today I'd expect something closer to 10%.
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The 'back then' argument sounds pretty convincing: nowadays every computer scientist knows the basics of logic reasoning, and most of them should be able to solve the riddle within at most a day. In Einstein's days, there was much less need to teach logic, and thus much less people familiar with techniques that are useful to solve these kind of riddles. I could easily believe that in the early 20th century only 2% of the world population could solve that. But today I'd expect something closer to 10%.
I'm still curious about a number in useful terms. For example, in "advanced" cultures in the age group 20-60, what percentage could solve it in 2 hours? This would exclude subsistence populations that have never been to school, etc etc. A raw number like "world population" isn't useful.
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I have to agree with the comment that Sudoku helps. It really was just a matter of elimination. Like most others here, I used Excel just to visually provide a canvas. I laid out all the clues as if they were pieces of a puzzle. With exception of one possible variable (the dreaded water drinker) they all fit nicely together. All said, I was done in under 10 minutes.
____________________________________________________ I'd rather have a frontal lobotomy than a bottle in front of me... Bill W
The hard part (for me) was realizing that it's indeed really similar to Sudoko. The rest was a piece of cake. Funny, I once read that the only thing repeatedly doing a 'brain game' achieves, is to get better at solving that particular brain game, but nothing else. Here's the proof that a brain game that isn't even very difficult (i. e. can be solved by the majority of people) can help you solve quite a broad range of much more difficult problems! Of course, as indicated above, not everyone who's good at Sudoko might realize how the Einstein riddle is connected to it...
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Tom Lawton wrote:
It helps if you do Sudoku regularly
Haha, that's what my friend said.
These kinds of logic problems can also be found in some crosswords books, although with fewer dimensions to deal with. They occasionally have tutorials that espouse the matrix approach to solving the puzzle.
I'm not a programmer but I play one at the office
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I'm still curious about a number in useful terms. For example, in "advanced" cultures in the age group 20-60, what percentage could solve it in 2 hours? This would exclude subsistence populations that have never been to school, etc etc. A raw number like "world population" isn't useful.
I don't know who made that statement in the first place, but I suspect someone added it later. Maybe they had a number of people do it, get the average IQ of those who could solve it, and then determine what percentage of people on the world have that high an IQ. That method would at least make some sense when talking of '2% of the world population', if indeed that was what the 2% were referring to. P.S.: just checked on the riddle again and it does indeed claim that Einstein himself made that '98% of the world population cannot solve it' statement. That makes my explanataion somewhat unlikely. My best guess is that is was an educated guess rather than accurate experimentally backed up fact.
modified on Thursday, December 9, 2010 12:35 PM
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One of the emails CP sends out linked to this (don't scroll too far down or you'll see the answer). Usually, I would be most interested in the programming portion, but for this particular puzzle I found the logic to be the most interesting part, so I decided to solve it myself. I solved it in 1 to 2 hours, but I'm not entirely sure if I cheated or not. Basically, I solved as much of it as I could using logic, then I tried a few possible combinations until I got a result that satisfied all the criteria (I assumed there was only 1 solution). Since I did it by hand (well, using Excel to quickly copy/paste), I'm thinking it wouldn't be considered cheating. In any event, it's a fun puzzle and I encourage you all to attempt it when you have a bit of time to focus (and report the results back here!). Also, that 98% of people would not be able to solve this seems silly. Do you think he meant 98% of people would not be able to solve this within a certain timeframe? Or maybe that only 2% of people could prove their solution without making the simplifying assumption that only one solution exists? If you want to see a solution fully explained, see here. Also, Wikipedia explains the solution to a variant of the puzzle. I have not read either, but thought I'd include those links for you more, erm, productive individuals. ;)
Not to make any feel bad but my 14 year old daughter had it solved in about 10 minutes. She is a big geek and scores in the 97%+ on assessments if that helps your ego.
Jerry W. Manweiler, Ph.D. Fundamental Technologies, LLC
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Not to make any feel bad but my 14 year old daughter had it solved in about 10 minutes. She is a big geek and scores in the 97%+ on assessments if that helps your ego.
Jerry W. Manweiler, Ph.D. Fundamental Technologies, LLC
The great thing about logic and reasoning ability is that they can be attained very early on. You should be very proud!
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The great thing about logic and reasoning ability is that they can be attained very early on. You should be very proud!
I am, she has a great future in front of her assuming she can get thru all of the teenage distractions.
Jerry W. Manweiler, Ph.D. Fundamental Technologies, LLC
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One of the emails CP sends out linked to this (don't scroll too far down or you'll see the answer). Usually, I would be most interested in the programming portion, but for this particular puzzle I found the logic to be the most interesting part, so I decided to solve it myself. I solved it in 1 to 2 hours, but I'm not entirely sure if I cheated or not. Basically, I solved as much of it as I could using logic, then I tried a few possible combinations until I got a result that satisfied all the criteria (I assumed there was only 1 solution). Since I did it by hand (well, using Excel to quickly copy/paste), I'm thinking it wouldn't be considered cheating. In any event, it's a fun puzzle and I encourage you all to attempt it when you have a bit of time to focus (and report the results back here!). Also, that 98% of people would not be able to solve this seems silly. Do you think he meant 98% of people would not be able to solve this within a certain timeframe? Or maybe that only 2% of people could prove their solution without making the simplifying assumption that only one solution exists? If you want to see a solution fully explained, see here. Also, Wikipedia explains the solution to a variant of the puzzle. I have not read either, but thought I'd include those links for you more, erm, productive individuals. ;)
As one of the commenters ("HMav") points out, there is no answer without making assumptions - none of the conditions requires that anyone owns a fish (four animals are specified - a dog, a cat, birds, and horses). It is an unsupported assumption that someone owns a fish. Also, the first commenter ("Alexey") notes that:
The main point of the Einstein’s Riddle is that 98% of human beings are unable to hold in memory more than 9 information units simultaneously ( whatever they could be ). Indeed, try to solve it using only your brain, and NOT using any other means ( such as paper, pencil, computers, etc.).
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One of the emails CP sends out linked to this (don't scroll too far down or you'll see the answer). Usually, I would be most interested in the programming portion, but for this particular puzzle I found the logic to be the most interesting part, so I decided to solve it myself. I solved it in 1 to 2 hours, but I'm not entirely sure if I cheated or not. Basically, I solved as much of it as I could using logic, then I tried a few possible combinations until I got a result that satisfied all the criteria (I assumed there was only 1 solution). Since I did it by hand (well, using Excel to quickly copy/paste), I'm thinking it wouldn't be considered cheating. In any event, it's a fun puzzle and I encourage you all to attempt it when you have a bit of time to focus (and report the results back here!). Also, that 98% of people would not be able to solve this seems silly. Do you think he meant 98% of people would not be able to solve this within a certain timeframe? Or maybe that only 2% of people could prove their solution without making the simplifying assumption that only one solution exists? If you want to see a solution fully explained, see here. Also, Wikipedia explains the solution to a variant of the puzzle. I have not read either, but thought I'd include those links for you more, erm, productive individuals. ;)
Took me about 15 mins with pen and paper.
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Took me a pencil, about half a page of hand-scribbled notes, and roughly 15 minutes to solve. My method involved figuring out a method to encode the statements into a Sudoko-like scheme (i. e. for every attribute I wrote down the list of house numbers they might be associated to) and then using the basic mechanics of exclusion to strike off every option that couldn't work until I ended up with an attribute that had only one option left. I created a table for the houses and attributes I already found out for each of them as an easy way to look up which of the attributes I already know of a house would conflict with a given statement. That is also how I would have solved it using Prolog. Not sure what the language was the author used, but the program looked awfully long and unneccessarily complicated. Would have been a lot shorter in Prolog! (although the neighbourhood relations might have been difficult to encode in Prolog as well) Regarding the 98% statement - I can easily believe that 90% of all people wouldn't know where to even start, as their skills to analyze a problem or logically reason is way below that of someone who came into contact with that kind of stuff beyond school. Any computer scientist, mathematician, and even most programmers without an academic degree know the basic tools required to solve this kind of problem, but very few other people have. The remaining 10% I would expect to be theoretically able to solve the problem, given enough time, but many might give up because they didn't come up with a suitable way to encode the problem, or kept on trying to solve it using direct implications, instead of looking at exclusion mechanisms. I'd still expect most of these people *could* solve it if their live depended upon it, and maybe after a good night's sleep ;)
The author used Scheme.
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As one of the commenters ("HMav") points out, there is no answer without making assumptions - none of the conditions requires that anyone owns a fish (four animals are specified - a dog, a cat, birds, and horses). It is an unsupported assumption that someone owns a fish. Also, the first commenter ("Alexey") notes that:
The main point of the Einstein’s Riddle is that 98% of human beings are unable to hold in memory more than 9 information units simultaneously ( whatever they could be ). Indeed, try to solve it using only your brain, and NOT using any other means ( such as paper, pencil, computers, etc.).
Regarding HMav, I disagree. If 'fish' were not one of the pets the question didn't even make sense. (unless you suspect a trick question) I do find it a bit unfortunate that there are quite a few spelling errors and ambiguous terminology in the riddle (for instance the interchangably used term of 'home owner' and 'person living in a house' - how do we know the German isn't renting out these houses to all of the others? Also the capitalized 'White house' - Are we talking of the one in Washington here? And what if someone had painted it blue? ;) As long as we know this is not a trick question we should make reasonable assumptions, and these assumptions have nothing to do with the riddle itself, only with the ambiguities of language, or simple typos. Regarding Alexey's statement, I also disagree. In this riddle you don't need to combine more than 3-4 of the statements at any one time to draw a conclusion for one additional bit of info. And nothing stops you from committing any piece of information to long term memory. It just takes longer than penning it down.
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One of the emails CP sends out linked to this (don't scroll too far down or you'll see the answer). Usually, I would be most interested in the programming portion, but for this particular puzzle I found the logic to be the most interesting part, so I decided to solve it myself. I solved it in 1 to 2 hours, but I'm not entirely sure if I cheated or not. Basically, I solved as much of it as I could using logic, then I tried a few possible combinations until I got a result that satisfied all the criteria (I assumed there was only 1 solution). Since I did it by hand (well, using Excel to quickly copy/paste), I'm thinking it wouldn't be considered cheating. In any event, it's a fun puzzle and I encourage you all to attempt it when you have a bit of time to focus (and report the results back here!). Also, that 98% of people would not be able to solve this seems silly. Do you think he meant 98% of people would not be able to solve this within a certain timeframe? Or maybe that only 2% of people could prove their solution without making the simplifying assumption that only one solution exists? If you want to see a solution fully explained, see here. Also, Wikipedia explains the solution to a variant of the puzzle. I have not read either, but thought I'd include those links for you more, erm, productive individuals. ;)
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Times like yours are an inspiration. I just bought a sudoku book. I plan on increasing my reasoning agility. :)
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Times like yours are an inspiration. I just bought a sudoku book. I plan on increasing my reasoning agility. :)
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One of the emails CP sends out linked to this (don't scroll too far down or you'll see the answer). Usually, I would be most interested in the programming portion, but for this particular puzzle I found the logic to be the most interesting part, so I decided to solve it myself. I solved it in 1 to 2 hours, but I'm not entirely sure if I cheated or not. Basically, I solved as much of it as I could using logic, then I tried a few possible combinations until I got a result that satisfied all the criteria (I assumed there was only 1 solution). Since I did it by hand (well, using Excel to quickly copy/paste), I'm thinking it wouldn't be considered cheating. In any event, it's a fun puzzle and I encourage you all to attempt it when you have a bit of time to focus (and report the results back here!). Also, that 98% of people would not be able to solve this seems silly. Do you think he meant 98% of people would not be able to solve this within a certain timeframe? Or maybe that only 2% of people could prove their solution without making the simplifying assumption that only one solution exists? If you want to see a solution fully explained, see here. Also, Wikipedia explains the solution to a variant of the puzzle. I have not read either, but thought I'd include those links for you more, erm, productive individuals. ;)
it took around 15 minutes with pen and paper
manoj sharma 0901371310 manoj.great@yahoo.com
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One of the emails CP sends out linked to this (don't scroll too far down or you'll see the answer). Usually, I would be most interested in the programming portion, but for this particular puzzle I found the logic to be the most interesting part, so I decided to solve it myself. I solved it in 1 to 2 hours, but I'm not entirely sure if I cheated or not. Basically, I solved as much of it as I could using logic, then I tried a few possible combinations until I got a result that satisfied all the criteria (I assumed there was only 1 solution). Since I did it by hand (well, using Excel to quickly copy/paste), I'm thinking it wouldn't be considered cheating. In any event, it's a fun puzzle and I encourage you all to attempt it when you have a bit of time to focus (and report the results back here!). Also, that 98% of people would not be able to solve this seems silly. Do you think he meant 98% of people would not be able to solve this within a certain timeframe? Or maybe that only 2% of people could prove their solution without making the simplifying assumption that only one solution exists? If you want to see a solution fully explained, see here. Also, Wikipedia explains the solution to a variant of the puzzle. I have not read either, but thought I'd include those links for you more, erm, productive individuals. ;)
There is one more unstated assumption to the problem, that the houses are arranged left to right with the 'first' house being on the left. Although according to Alex Miranda (http://ticsblog.com/2010/12/07/solving-einsteins-riddle-using-nondeterministic-computing/) apparenlty, the solution to the riddle is identical in either case. At least we know that the houses aren't arranged in a circle/pentagon ... Took me about 45 minutes, most of it spent setting up the matrix of options and turning it into a picture puzzle. Powerpoint is a very useful tool for many things.
modified on Tuesday, December 14, 2010 2:37 PM
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There is one more unstated assumption to the problem, that the houses are arranged left to right with the 'first' house being on the left. Although according to Alex Miranda (http://ticsblog.com/2010/12/07/solving-einsteins-riddle-using-nondeterministic-computing/) apparenlty, the solution to the riddle is identical in either case. At least we know that the houses aren't arranged in a circle/pentagon ... Took me about 45 minutes, most of it spent setting up the matrix of options and turning it into a picture puzzle. Powerpoint is a very useful tool for many things.
modified on Tuesday, December 14, 2010 2:37 PM
Indeed. Took me a while before I accepted the assumption that all the houses were side by side (why not positioned like an "L"?).
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There is one more unstated assumption to the problem, that the houses are arranged left to right with the 'first' house being on the left. Although according to Alex Miranda (http://ticsblog.com/2010/12/07/solving-einsteins-riddle-using-nondeterministic-computing/) apparenlty, the solution to the riddle is identical in either case. At least we know that the houses aren't arranged in a circle/pentagon ... Took me about 45 minutes, most of it spent setting up the matrix of options and turning it into a picture puzzle. Powerpoint is a very useful tool for many things.
modified on Tuesday, December 14, 2010 2:37 PM
I don't think the first house being on the left is such a big thing to 'assume', although you have a point when considering people using languages that are written right to left
Michael Waters wrote:
At least we know that the houses aren't arranged in a circle/pentagon ...
Now, the riddle did mention the White house, now that you mention it... ;)