Math.dartmouth.edu



One Step at a TimePuzzles, especially number and math puzzles, can be fun, intricate and challenging. Some people enjoy solving puzzles slowly over time and others enjoy conducting rigid, methodical analysis. There are many types of puzzles and usually numerous ways to find each puzzle’s solution. The key is to look at each puzzle in creative and efficient ways. By visualizing the problem to be solved, using the process of elimination, breaking down puzzles into smaller units, and methodically working through the remaining options, a puzzle solver can zero in on the solution. There is rarely just one solution to any puzzle, but there are methods that can make solving nearly every puzzle easier.In my opinion, the best way to increase the success of solving a puzzle is to create a “pen and paper image” of the problem to be solved. Visualization is the key. Seeing a graphic representation of the puzzle on a sheet of paper can emphasize patterns, trends, and solution methods; it also reduces the likelihood of the puzzle solver making “silly” mistakes. Creating a model of the puzzle also promotes deeper understanding of the concept and how to solve it, rather than just rote memorization of the solution path(s). Some puzzles, like the “Seven City” puzzle, cannot be solved without creating an illustration or model; it is nearly impossible to solve in a person’s head. The goal of “Seven Cities” is to find one way to go through seven differently laid out cities. The solution to the puzzle is much too intricate to solve in one’s head; mistakes would eventually be made. The puzzle “Tic Tac Toe (closest to 15)” has the solver pick numbers from 1-9 and add them up in a tic-tac-toe format until the three numbers in each row equal 18. “Tic-Tac-Toe (closest to 15)” can be solved mentally but the solver would have a better chance of success if he or she created a graphical representation on paper. While it seems difficult at first, practice leads to more success with the strategy.Another technique for solving puzzles is the process of elimination. The object of this method is to reduce the number of possibilities for a given puzzle step logically. For example, in the commonly known puzzle Sudoku, you are consistently eliminating possibilities by filling in rows and columns with the digits 1-9. Each time you place a number in a box, you are eliminating the option of that number appearing in any other cell that is situation within that cell’s corresponding grouping, row and column. If the solver doesn’t narrow the options by eliminating possibilities, even a Sudoku puzzle becomes nearly impossible to solve successfully. Eliminating choices is a key strategy.Another successful puzzle-solving strategy is breaking down puzzles into smaller units in order to solve them efficiently. When we explored more challenging puzzles in class, we discovered the need to use several elimination methods. A good example of this is the “Couples Shaking Hands” puzzle. In this brainteaser, a man and his wife go to a party where there are four other married couples. Every person shakes hands with everyone with whom they were not previous acquainted. After the handshaking, the man asks everyone, including his wife, how many hands they shook. Knowing that no man or women of the same couple shook each other’s hand, he gets nine different answers. The question is how many hands did the man's wife shake? It is important to visualize this problem, but the best way to solve this puzzle is to start small. Start by solving with one couple, following the guidelines, and expanding from there until you solve the puzzle entirely. The puzzle is too complicated for most people to solve in their head; the solution is much easier to “see” when the map of the puzzle is drawn out. If you attempt a trial and error method by drawing lines between people and not trying it with smaller numbers first, the puzzle far more difficult than it has to be. The Smaller Pieces Method is best used when organizing the data into more manageable chunks minimized the puzzle’s complexity. People work on puzzles in different ways and for different reasons. Some people try to find puzzle answers as quickly as possible, and some solve puzzles to follow a methodical process of elimination. Likewise, some solvers want to exercise their brain; some are looking to reduce stress. By visualizing the problem to be solved, using the process of elimination, breaking down puzzles into smaller units, and methodically working through the remaining options, a puzzle solver can zero in on the solution. ................
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