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Vinit Kumar

Hard Problems And How To Solve Them

February 05, 2020

Every once in a while, we encounter a problem that seems very hard to solve and at the moment we have no clue how to fix them.

Two options comes to our mind when we are in such situation:

  • Give up and loose all hope of solving the problem.
  • Hold your ground and try and solve the problem.

However, it is not so simple and requires much steps than just trying.

Whenever, I face such a challenge I try to assess the situation and think deeply about it. Is the problem actually very hard and does it only seems hard due to my unfamiliarity with the problem. If such is the case, the first obvious way to tackle it would be get familiar with problem space and note it down. In almost 90% of the cases, this approach will give your more clarity and confidence in your abilities.

In other case, where upon assessment I realize that the problem is actually very hard to solve, the first approach I apply is “divide and rule” and break the hard problem into smaller problems that are a subset of the bigger problem. And I then ensure that the smaller subsets are self contained and form non-intersecting sets. Then, I start solving the problem subsets from in the order of easy to hard. As I start solving the problem, I gain in confidence and also have more clarity about the bigger problem. Mind that, I also need to refer theory and texts about the subsets as well since it is outside my comfort or knowledge zone.

In the third case, I might not be able to solve all parts and might have misunderstood the problem. This might be frustrating experience, but it is also a great opportunity to reassess my strategy and leave the problem as it is and try and tackle it later. Sometimes, I am able to think of a novel idea when thinking about the problems from a fresh mind and perspective.

© 2023, Vinit Kumar