The 3 Most Common Controversial Problems of Math

Fresh problems in the house!

Image result for what if I told you I had the same problem meme

Have you ever wondered whether all the problems in your math class were solved, or perhaps in the ENTIRE world itself?

Okay, okay, chill. Might sound obvious, yet, it is NOT false. Yep, just like that, Jimmy (AKA Russian Comedy Club). They were all solved, but not all were accomplished.


There’s nothing better than a tiny portion of humor while explaining tough concepts

Today we will be observing the 3 most ‘odd’ mind-blowing problems that specialists believe to be excessively controversial. There is no time to waste, hence here comes the meatloaf!

#1: The monty hall problem

Thesis: Let’s say you’re on a game show where the host shows you 3 doors. Behind one of these doors is a brand new car (“…Lada Sedan!…Baklajan“). Behind the other two are goats. You get to pick a door. Then, the host will open one of the doors you didn’t open to reveal one of the goats (say behind the blue door below).


Then he asks you: Do you want to switch doors? Or do you want to stay with the door you chose?


Your first thought might be to stay with the door you chose, involving the logic of human heuristics, thinking:

  • “It’s worked out pretty well so far, right?”
  • “Since there are only 2 doors at this point, it’s a 50/50 shot at winning the car.”

Is this the correct way of interpreting this situation? Turns out it’s not.

The best strategy with the game is to switch. Every time.

A player whose strategy is to switch every single time will only lose when the door they initially selected had the car behind it.

Since the odds of choosing the car on the first move are 1/3, the odds of losing the game when you switch every time are also 1/3. This means that a person who switches every time will win 2/3 of the time, which makes it DOUBLE the odds of winning of the person whose strategy is to stay every time.

Image result for stop lying meme

Now, I know there are some of you who tend to demonstrate an even harsh look from this fella above, and keep stating that it is inevitably WRONG (I had the exact same reaction in the beginning). Let’s give the job to my fair-well friend… “Business Insider”! *Applause everyone, applause*

*Denzel Curry’s song “Ultimate” blasts into the scene*


#2: How to estimate π (pi) from a dart board

Dart Games

NO, NO, NO don’t even think about playing darts until you finish this article… I got my eyes on you…

One of the most interesting ways to estimate the value of π is by repeatedly randomly selecting points within this square.

  • The circle inscribed in the square has a radius of 1. The Square has a side length of 2.

This means that the area of the circle is:                S1 = π*r*r = π*1*1 = π 

And the area of the square is: S2 = 2*2 = 4

Next, we randomly select thousands of points from within the square or, to get a good approximation, doing this a million times.

*Yo, stop laughing! We’re talking deep math*

Once you’ve repeated this, to approximate the value of π plug your results into the following formula:

π/4 = (Number of points within the circle) / (Total number of points

This uses geometry and probability to estimate π.


#3: the broken water heater problem

Thesis: “Last week, the heat in my apartment crapped out because my water heater broke. I went to a person, showed him the water heater, he used a bunch of spare parts and then fixed it. I paid him for the repairs.”

Dilemma: Is this person more likely: an Accountant or an Accountant AND a Plumber?

Image result for guess meme

Alright, assume we chose it is more likely he’s an Accountant:

  • Since the scenario makes it sound like the guy is a plumber, you intuitively thought that he’s a plumber.
  • However, anyone who is “an Accountant AND a Plumber” is also an Accountant.

Strictly speaking, it’s more likely that he’s an Accountant than a Plumber because:

  • The probability “A” that the guy who fixed my water heater is both an  Accountant AND a Plumber is already factored into the probability that the guy who fixed my water heater is an Accountant.
  • There’s also the probability “B” that the guy who fixed my water heater is only an Accountant NOT a Plumber



Thank you all for reading this article, hope I was able to eliminate some boredom out of yourselves for the sake of prosperity (kidding). Feel free to leave any comments below and let me know if things sounded prosaic to have me give a better snack next time!


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Written by Shohruh Artaman
A typical writer illustrating typical principles
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