“A world without problems is an illusion, so is a world without solutions”
- G. Sarcone

Sarcone & Waeber’s rules to puzzle solving

• Nothing is as difficult as it looks.
• Nothing is as easy as it looks.
• Read the instructions carefully in order to avoid giving the right answer to the wrong puzzle.
• Human languages were not 'designed' for logical clarity. Remember that each topic within math (or within any field) has its own tricky phrases.
• Recognize clearly what you have to search for, what data is useful and what are the relationships between the searched result and the data.
• Misdirection is very common in puzzles. Expert puzzle authors always try to lead people's minds along false trails.
• Elements that appear to have no relevance may be fundamental and vice versa.
• Omissions (what is not written or said) are sometimes as important as the instructions given.
• Beware of subconscious restrictions and mental blocks, try to depart from the norms and stereotypes and look beyond the boundaries of a problem.
• Break a complex puzzle into smaller, manageable parts.
• Ensure that the puzzle has been considered from all points of view.
• In logic, correlation does not always imply causation, that is:
   - Correlated elements or events are not necessarily related. Some could be just coincidence.
   - Likewise, correlated events may have a common cause. In fact, some correlations may not be relations between cause and effect but represent two effects of some other cause.
   - Either of two correlated events may cause the other.
• Sometimes, to understand a problem, you'll need to use collective intelligence. Do not hesitate to ask someone else to help you.
• Use your intuition and deliberately try to find other ways to solve a puzzle.
• Sometimes, the solution is what causes the problem. Avoid finding solutions to nonexistent problems, and never fix what is not broken.
• Enjoy making mistakes. Regard them as important and fruitful stages on the road to success.
• Be persistent, the joy of achievement is greater when it is preceded by a tough creative effort!
• Puzzles always have one, several or no solutions.
• Fortunately, there are sometimes acceptable alternative solutions to problems/puzzles with no solutions. In this case, non-standard or indirect but creative approaches can be very useful (see multiple thinking patterns).

Have fun and good luck!

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Source: Puzzillusions, © Sarcone & Waeber, Archimedes-lab.org, and Carlton Publishing.

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