This is a series of my notes on graph theory and usage in Scholarship Problems. We look at what a graph is today and present some terminologies. We also present some basic tactics to solve elementary problems. Following the tradition of this blog, we do not present any illustrations on using the tactics as it limits the readers to thinking about the problems only through a specific approach whereas in an exam environment multiple approaches and various combination of techniques is necessary.

In this post we take a dive into building a very minimalist toolkit which might be useful for Diophantine Equation problems. This write-up especially focusses on the easier side of things related to cater Scholarship problems and not Olympiad Problems which may require various additional specialised methods. We do not illustrate any methods with examples since it is often quite restricting to see a few examples and become limited to one such method, whereas in an exam environment multiple trial with several approaches are almost always necessary.

Often-a-while fibonacci sequence problems stars as the guest problem in olympiad exam papers and often the solution is hidden from the untrained eye as some form of application of its properties. This article assumes familiarity with the definition of the “Fibonacci Sequence” and the ability to comprehend recursive definitions at the minimum. We will present various properties related to Fibonacci Numbers (and related) without any proof. It is the interest of the reader to seek out the proofs and validate each result for their own.