Solving 'Hundepuzzle' with High School Maths Only

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The discussion revolves around the "Hundepuzzle," a card game involving the arrangement of 9 cards depicting different dogs, where the goal is to match the cards' orientations. Participants debate whether a solution can be derived using only high school mathematics, with some suggesting that a procedural algorithm may be more suitable than a strict equation. There is contention over the number of solutions, with some asserting that rotating the entire arrangement yields multiple solutions. The conversation also touches on the concepts of brute force versus algorithmic approaches to solving the puzzle, highlighting the efficiency of backtracking methods. Ultimately, the forum seeks to explore the mathematical principles applicable to this puzzle without delving into higher mathematics.
  • #31
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.

I used numbers {1,2,3,4} for heads and {-1,-2,-3,-4} for tails instead. That makes matching cells much easier. I used if(one_cell == -the_other_cell) but I could have obfuscated it with something like if(!(one_cell+the_other_cell)) for a more C-ish look.
 

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