This is a slight overview on how you should approach a problem based on my experience. And what are the things you should be ready be with if you are unable to solve it.

Some of Them are from the based on the book and additionally added by me.

Reading the problem statement correctly is very important. It’s very easy to miss a few lines or misinterpret and completely miss the solution.

Here are some points to get started.

This overall starts with defining the problem Structure of the given problem.This includes all the observable axioms and overall how the problem moves through different states. You have to observe the movement by getting your hands dirty and propose conjectures based on them. They need not be true or false but they must be proved.

Make claims, prove them, Or disprove them.

“If You can’t a solve a problem, there exists an easier version of it which you can, find it!” - Polya.

Concentrate on the key difficulty of the problem. What makes it so tough? And what if I remove it. Then if you have a solution, can we extend it. What are the most obvious used ideas? A few strategies may include

• Make all the elements same.
• Lower the Constraints
• Making things monotonic.
• Solving with The Extreme Principle.
• Making Things symmetrical.
• Increasing or Decreasing the number of invariant.
• And the all powerful, Simplify.

After the restate and rephrase part, try to notice what are the factors that do not change with time. Looking at the final result can also be very helpful for find invariants and mono-variants.

Reduction is the method to convert a problem statement into a reduced problem statement. In easy problems, you'd find problems being reduced to very standards problems we know of.

Asking relevant questions lead us to observations, these observations are then used tranpose the problem statement into something we already know and can work upon.