Einstein's Riddle (A Challenging Logic Puzzle)
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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... ;)
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Indeed. Took me a while before I accepted the assumption that all the houses were side by side (why not positioned like an "L"?).
How about 4 of the houses at the corners of a tetrahedron, and the fifth using one side of that tetrahedron to build another tetrahedron on (so you get two tetrahedron glued together on one side). The result would be that all houses would be 'next' to each other, except one particular pair. Or for simplicity's sake, why not have 4-dimensional houses (the riddle didn't demand they're 3-dimensional!) aligned on the vertices of a 4-simplex (the 4D-equivalent of a tetrahedron)? Then each pair of two houses would have the exact same distance, and in that sense would be 'next' to each other. :cool: Ok, it wouldn't work however, since statement 4 uses the relation 'next to and to the left of', which in turn implies that there is at least one houses that is left to another house, but not next to that same house! Now, if you make the assumption that the 'left to' statement implies that all of the houses can be compared in a 'left to' relation, then you could derive the houses are an ordered set, and therefore can be arranged in a sequence (independent of their actual geographical positions - they could for instance be houses along a serpentine road, and the 'left of' could be from the viewpoint of someone driving along that road; think Google Streetview ;)). However, this would be just that, an assumption: there is nothing in the riddle that prohibits e. g. 4 of the houses standing in a square arrangement, with 1 and 2 in the front and 3 and 4 in the back: here 1 would be left of and next to 2, but 2 is 'left of' no other house. Also, 3 might be behind house 1 and thus neither to the left nor right of 1, although it's next to 1. This is where we have to decide whether we are looking at a trick question, which deliberately uses such ambiguities, or whether this is a 'serious' riddle. In the latter case, as it is often tedious to restrict every unusual possibility someone might think of, you should always assume the context of the riddle is the most simple that is consistent with the statements and facts provided. In this case: - Houses are standing in a row (or a wavy line if you prefer ;)) - The home owners are each owning only one of the houses and living in it as well (the riddle uses 'living in' and 'ownership' interchangably) - The occasional use of capital letters on various color attributes are just typos and do not indicate names (such as in the 'White House') - the leftmost house is number 1 (no, Einstein did not write right to left) - There's only one person living in each house (whil