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Think outside the box

Once you are stuck on a problem have start to believe that there is no possible solution, it is all too easy to start blaming external things: maybe the question is wrong, has a typo in it or something; maybe you were not given the right tools to solve it... But this kind of thinking won't get you anywhere! And you have to admit that it is very very unlikely that the problem comes from the outside; most of the the time it is just you that is missing something.
The first step to get unstuck is to admit that the issue is not coming from the problem itself, but just from your understanding of it. Once you accept that you can start to reason clearly about it and try to find the missing piece in your understanding.

Once you are at that point, try to re-evaluate every option, and don't discard any prematurely: double check all your assumptions! Often I you feel like a problem is impossible it is because you have discarded an option based on an assumpion you had.

If the problem has only a few possible solutions, once you definitely crossed out the ones that cannot work, you will necessarily be left with the right solution. If this last solution doesn't seem to work either for you, don't let your brain freeze and try to understand how it could work! This is the moment where you discover your hidden assumptions and why they were erroneous.

Exercises​

  • Code Combat, Introduction to Computer Science, exercises 3a and 3b (Create a teacher account to play for free)
  • How to make exactly 4 triangles with 6 matches? (NB: a triangle is formed when the ends of the matches touch) (NB: the triangles must all have the same size (1 match per side))
    TIP
    Think in 3D
  • Can you connect the four dots and return to your starting point with just three straight lines, without lifting your pen from the paper or retracing your steps?
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  • TODO check in the book "Beauty of Math" I think they have a similar example
  • There are ants on a rod: the rod is 1 meter long and the ants walk 1 meter per second. When two ants bump into each other, they take a half-turn and continue in the opposite direction. Once they arrive at one of the ends of the rod, they leave. Question: how long will it take for all the ants to leave? TODO put a drawing to show the starting positions and directions of the ants
  • Can You Solve These "Ghostly" Riddles? - MindYourDecisions

Going further​

Pragmatic Programmer, Chapter 8, Item 46: Solving Impossible Puzzles