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pioneerboy
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Is there a solution to this game https://prlbr.de/2011/08/hundepuzzle/alle-karten.png in the form of an equation that only requires high school mathematics but no higher maths and informatics?
Can you translate the description of the puzzle which is one level up from that figure's URL?pioneerboy said:Is there a solution to this game https://prlbr.de/2011/08/hundepuzzle/alle-karten.png in the form of an equation that only requires high school mathematics but no higher maths and informatics?
May we also assume that the top edge must correctly mate with the bottom edge and that the right edge must correctly mate with the left edge? (as if the 9 cards were arranged on a torus).pioneerboy said:Sure. It's very easy and does not require literal translation.
You have 9 cards showing the front or back of 4 different dogs. The cards must be layed and turned so that all fronts and backs that do not touch the 9x9 card's corners or edges are complete in the sense that they match the same dog. I read somewhere that there are two solutions.
However, I am not interested in the solution 'per se' but in the equation(s) leading to those solution(s). I am wondering if there are formulas that does only require high school mathematics without any stuff at all that is taught in college - higher maths, statistics, informatics etc. Or at least an explanation about what is the very lowest level that would be needed for such equation(s). I do not ask out of lazyness, but of curiosity if there's an understandable equation for people without having studied maths and informatics and try to find an equation on the back-of-an-envelop.
No. Unmated edges need not match.jbriggs444 said:May we also assume that the top edge must correctly mate with the bottom edge and that the right edge must correctly mate with the left edge? (as if the 9 cards were arranged on a torus).
Yes, I think he's looking for an algorithm.jbriggs444 said:You ask for an "equation". But It would seem more plausible that what you are after is a procedure by which the puzzle can be solved simply and efficiently. Is that correct?
Spoken like a mathematician!Vanadium 50 said:I also don't see how there can be as few as two solutions. Since you can always rotate the entire thing by 90 degrees, if there is one solution, there are four.
jbriggs444 said:May we also assume that the top edge must correctly mate with the bottom edge and that the right edge must correctly mate with the left edge?
Yup. That would be a brute-force technique. One wonders if there is any way to do it more parsimoniously.Vanadium 50 said:I would program this using backtracking.
Pick a tile and an orientation. Place the next tile down, and the next, and the next until either I have violated the rotation rule or cannot legally place another tile. Then back up as far as I need to, changing first the rotation and then the tile, until I get a success.
DaveC426913 said:hat would be a brute-force technique.
It is the brute force technique. Although I grant that is it not automatically slower than a solving algorithm.Vanadium 50 said:I differ.
Disagree. In many situations, mathematical proofs can find every solution without exhaustive tests. In fact, exhaustive tests are often insufficient to prove there are no more solutions: One can prove there are only 5 platonic solids. A brute force technique could never find every solution since you could count to infinity without proving there isn't another one hiding.Vanadium 50 said:Furthermore, if you want every solution, you are going to need some sort of exhaustive test.
DaveC426913 said:But brute force is not a rigorous mathematical proof.
DaveC426913 said:But brute force is not a rigorous mathematical proof.
I should have said brute force is not always a rigorous proof. And I was looking for an algorithm that would do for ALL puzzles of this type (I don't know how many there are - there might be one, there might be fifty).micromass said:Wow, are you serious? Brute force is not a rigorous mathematical proof? This is an insane post.
DaveC426913 said:I should have said brute force is not always a rigorous proof.
But it only works if there are a limited set of configurations.micromass said:It doesn't really sound like you understand brute force/rigorous proof. If you obtain a solution by brute force, then it's a rigorous proof.
DaveC426913 said:It only works if there are a limited set of configurations.
If you applied a brute force technique to discovering the Platonic solids, you would never finish, since, after hitting the first five, you could never be sure there weren't more based on a 100-sided or thousand-sided polygon.
OK, I would not have labeled that as brute force.micromass said:Here is a proof of the uniqueness of the Platonic solids that most mathematicians would consider brute force:
DaveC426913 said:OK, I would not have labeled that as brute force.
DaveC426913 said:You stopped at 6. You had to know rules about defect angles etc of polyhedra to stop at six. Brute force would have had you continue 7 and beyond.
My suggestion was to look for the same kinds of rules so that, like your example, we could know when a configuration fails without examining every permutation.
Not necessary. I grant the mathematical definition. Yes. Van's method works.micromass said:Please read this wikipedia article before replying further:
DaveC426913 said:there are other ways that might help solve the OP's puzzle.
bahamagreen said:See Wang Tiles...
pioneerboy said:y, I can't contribute to the solution as such else than an algorithm might be best built up upon the declaration of the 4 dogs as letters A, B, C, and D and the differentiation of heads and tails into small and large letters (a, b, c, d, A, B, C, D), whereas on a card heads and tails are always opposite of each other and two neighbouring cards would result in a whole dog of the form of e.g. a¦A.
High school math involves a variety of concepts and problem-solving techniques that can be applied to different situations, including puzzles. By using logical reasoning, algebra, geometry, and other mathematical principles, one can approach and solve puzzles in a systematic and efficient manner.
The 'Hundepuzzle' is a popular puzzle that involves arranging a group of dogs in a specific formation using only mathematical operations. It is challenging because it requires a combination of logical thinking and mathematical skills to determine the correct arrangement.
Yes, the 'Hundepuzzle' can be solved using only high school math. The puzzle is designed to be solved using basic mathematical concepts such as addition, subtraction, multiplication, and division. No advanced mathematical knowledge is required.
One strategy for solving the 'Hundepuzzle' is to start by identifying the given information and using it to narrow down the possible solutions. Then, use logical reasoning and mathematical operations to eliminate incorrect options and find the correct arrangement. Another strategy is to work backwards from the desired arrangement, using inverse operations to determine the necessary steps to get there.
Solving the 'Hundepuzzle' with high school math can improve problem-solving skills by encouraging logical thinking, critical reasoning, and mathematical fluency. It also demonstrates the practical application of math in real-life situations, which can help students develop a deeper understanding and appreciation for the subject.