Wednesday, November 04, 2009

Puzzling Puzzles

Recently I watched a TV show in which the main characters come to puzzle to get a device they want. The puzzle consists of a three by three matrix and nine stones with the number 1-9 written on them. They come to the conclusion that what they need to do is arrange the stones so that in every direction including the diagonals the value of the stones sum to 15, where if they where wrong when they tried to open the compartment that the puzzle was the key to they would be poisoned.

Last week I was in the mood for a good puzzle while bored in an engineering project management course so I decided to take a crack. After a couple of tries consisting of an initial random guess then working out from there I struck on a strategy and found a solution that was almost perfect except that one of the diagonals summed to 12, so I did it once more and found a solution. However, I looked at it and came to the solution that the characters only had a one in eight chance of getting the exact solution with only the center stone fixed. The reason for this is that the rotation or flipping about the center lines will also give a valid solution, so that there is a set of eight dependent solutions. I find this funny because they where talking about the same question having been on a MENSA exam (which caused me to take a mental workout exam on the MENSA website, also a fun endeavor). In this case the center stone/number was given to fit into the center slot and my solution ended up with that value in the center. I have two challengers for you readers find a solution to this problem and determine if there are multiple independent solution sets (where the center values are different between the two sets). The second one is a different puzzle entirely that was given to me by a friend who had gotten it in class (he was told that anyone who solved it would not have to take the classes final and that only one person had done it in the past). It goes as such, you have three houses and three utilities. The objective is to connect all three houses with all three utilities without crossing any of the lines as it is in a 2-D world.
Good Luck to all (just don't spend to much time on the last problem). Plus bonus points to anyone who knows what show this is from.

13 comments:

  1. folding the paper allowed??

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  2. no paper folding allowed

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  3. You realize that the second problem is a topological impossibility, unless of course pipes go through houses on the way?

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  4. The show is probably "Lost". I hear it is full of poorly thought out puzzles.

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  5. you should be careful trying to solve puzzles in favorite programs. I once decided to track all the plaid suitcases in What's Up Doc?' & discovered they never could have been mixed up the way they were. & now I am a little bit sad every time I watch that movie.

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  6. That's nothing. Harry Potter was never the same after I discovered that the chess match and logic puzzle were impossible and insolvable respectively. Well actually, I realized that pretty much immediately, but I'm sure ignorant bliss would've made the book more enjoyable.

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  7. Do you have to connect them with straight lines?

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  8. I can think of a 2D world where the puzzle is solvable. But you said no bending the paper, so I'm not sure if it counts.

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  9. Eli, the surface of a torus is probably cheating. It also involves more than just bending the paper.

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  10. Why is it cheating? A torus is a 2D surface, and technically Aryeh never said anything about a piece of paper - that was Yoni's assumption.

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  11. Ok, lets put it this way the problem is on paper as per Yoni's assumption. However, let have an additional competition to find the most creative way to do it on some other 2-D surface.

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  12. As Elon said, on a flat 2D surface like a paper it's topologically impossible.

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  13. yes, hence my first comment!

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