Working Backwards: Recursion, Induction, and Minimality

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Explanations 9

Let′sLet'sLet′s talktalktalk aboutaboutabout methodsmethodsmethods ofofof proof!proof!proof! Probably the most common techniques are: ProofProofProof by:by:by: ContradictionCont…
By Evan Tong
Induction (Part 1) Table of Contents of the induction series : Part 1 Part 2 Part 3 Part 4 Part 5 Part 6 Part 7 So, what is induction? You might wonder, what is induction? This …
By Zi Song Yeoh, Alex Federspiel, Victor Wang
Induction (Part 2) The link to the table of contents. In the last post, we look at what induction is and gave a simple example of induction in action. In this part, we'll look a…
By Zi Song Yeoh, Expii Team, Alex Federspiel, Victor Wang
Induction (Part 3) Link to table of contents In this part, we'll look at strong induction. Strong induction Forgive me that I can't find a very good photo analogy of strong indu…
By Zi Song Yeoh, Victor Wang
Induction (Part 4) Link to table of contents In this article, we'll look at an interesting problem that can be solved by strong induction. A player AAA plays the following game …
By Zi Song Yeoh, Victor Wang
Induction (Part 5) Link to table of contents Sometimes you tried to solve a problem by induction, but unfortunately failed. You're frustrated. You give up, and get a 0/7 for tha…
By Zi Song Yeoh, Alex Federspiel, Victor Wang
Induction (Part 6) Link to table of contents In this part, we'll look at pitfalls of using induction. Pitfall #1 : n = n + 1 What is wrong with the following argument : We prove…
By Zi Song Yeoh, Victor Wang
Induction (Part 7) Link to the table of contents In this article, we look at two tougher problems. The plane is divided into regions by straight lines. Show that it is always po…
By Zi Song Yeoh, Alex Federspiel, Victor Wang
Introduction Recursion is a rather underestimated technique in math, especially in competitions. Perhaps it's because it sounds so vague or trivial on first hearing. So before I…
By Ivan Hu