How to crack Mathematical Puzzles

What are Mathematical Puzzles?
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Puzzles are entertaining opportunities to practice a clear thinking as well as enjoy the fruits of such activity. It consists of some jumbled facts and other relevant data. You are required to deduce an organized structure from the given information. Puzzle solving enhances diverse thinking and logical reasoning ability.
Mathematical puzzles involve the basic concepts of algebra, arithmetic, probability, time & distance, etc. You need to be aware of the fundamental mathematical concepts and formulae. Sometimes, you will need to rely on your lateral thinking ability rather than calculating efficiency.
Steps to crack a Mathematical Puzzle:
  1. First and foremost, read the entire problem carefully, because the introduction usually contains your first clues for the puzzle, or defines important parameters for the puzzle.
  2. Work out a particular structure of relationships. Organize the information in a schematic manner by using tables, symbols, and diagrams.
  3. Read all the puzzle clues, marking obvious associations, or eliminations, on the graph.
  4. Also, read back through the clues, applying any additional context you gleaned from later clues to the earlier clues as well.
  5. Watch for subtle gender clues based on names or pronouns. A clue like, "Neither Archimedes nor the physicist lives in the red house" includes the frequently overlooked information that Archimedes is not a physicist.
  6. Continue going back over the clues, gleaning additional information with each pass by applying the context you established on the previous passes.
  7. After having entered information from all the clues in the solve charts, read everything again. This helps you to identify more clues.
  8. Do not get stuck to a problem. It makes you lose valuable time. You may actually be on the wrong track altogether.
  9. One way to get "unstuck" is to make an assumption. If possible, find one to make which has been narrowed down to 2 possibilities. Assume one of the possibilities and continue trying to solve the puzzle under that assumption. If you encounter a contradiction, then your assumption was wrong and you can proceed from there knowing the other possibility must be true. If you complete the puzzle, then your assumption was right and you have solved the problem.
  10. Don't spend too much time practicing the same kind of questions. Instead, practice a variety of questions that you can recall later.
  11. Always keep in mind that the puzzle will give you all the information that is necessary to solve it. As frustrating as the puzzles can be, taking time to read through the facts carefully and periodically during your attempt can make matters easier.
Puzzle problems come in varying degrees of difficulty. With a good practice, you can help strengthen your reasoning skills and get better at logic problems. You will also know when to leave a puzzle alone if you are stuck. Sometimes leaving a puzzle and returning to it with fresh eyes and mind can help lead to more deductions and conclusions.
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