Ah, the pigeonhole principle. There’s a good chance you know of this, but in case you haven’t (or you just “forgot” apparently, showing off in front of your friends even though you’ve never heard of it before), here it is, in simple words:
You (Shouldn’t) Lose 2 – Zero Sum
Irrational Thinking
The simplest questions to understand are sometimes the toughest to solve. Have a look at this one:
May an irrational (number) raised to the power of an irrational ever result in a rational?
The first time I laid my eyes on it, I sat and thought for a moment. All I had to do was provide an example which satisfied the premise, and I was done. Or prove mathematically that it would never occur, of course, which seemed infinitely tougher.
Minor Differences: 0.999… and 1
An age old question has been asked several times over the history of mathematics. Mostly to gullible high-school students who are stereotypically scared of math and numbers, but it has been asked nonetheless. This diabolical question seems simple, but don’t be fooled by its simplicity, or any other -plicity.
You (Shouldn’t) Lose 1 – Rook Game
An interesting part of game theory is the concept of forced wins in two-player games. This means that at one stage, a player can make a series of moves in the game that will surely result a win, regardless of what the other player has up his sleeve. There’s been a lot of study about this, for example, on the endgames in chess.
Here, we’re gonna play one game in particular, that we define ourselves.
Random Coincidences 1 – Funny Fractions
Numbers are funny. Even with all the order and the systematicness, you will always find numbers cropping up in the most unexpected places. To look at some of these remarkable instances is the purpose of this series.
Let’s start off with something simple. Everyone knows how to reduce fractions to their simplest form, right? But what if I was annoyed at the conventional simplification, and started doing this?