# Understanding and Solving a Viral Logic Puzzle
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Chapter 1: Introduction to Logic Puzzles
Recently, I came across an engaging logic puzzle by Presh Talwalkar that piqued my interest. I thought it would be enjoyable to tackle this challenge together!
Let's break down the problem systematically.
Section 1.1: Understanding the Variables
In this puzzle, we define variables to represent the number of students selecting different subjects. For instance, let Cf denote the number of students who chose Chemistry and French.
Here’s what we know so far:
- 60 students opted for Physics and Mandarin, which gives us Pm = 60.
- A total of 100 students selected Chemistry, implying Cf + Cm = 100.
- The number of students who picked French is double that of those who chose Mandarin, leading to the equation: Cf + Pf = 2(Cm + Pm).
- Additionally, 120 students chose either Physics or Mandarin but not both, so we have Pf + Cm = 120.
What we aim to find is the overall number of students, represented as T = Cf + Cm + Pf + Pm.
Section 1.2: Solving for the Total
Since we already established that Pm = 60, we can express T as T = Cf + Cm + Pf + 60. Using the earlier equation, Cf + Cm = 100, we can reframe it as T = 100 + Pf + 60, which simplifies to T = Pf + 160.
Now, we need to determine Pf. We have two key relationships:
- From Cf + Pf = 2(Cm + Pm), we can express Pf as Pf = 2(Cm + 60) - Cf, simplifying to Pf = 2Cm + 120 - Cf (Equation I).
- From Pf + Cm = 120, we can rearrange this to get Pf = 120 - Cm (Equation II).
By subtracting Equation II from Equation I, we derive 0 = 3Cm - Cf, which simplifies to 3Cm = Cf (Equation III). We also know from our previous findings that Cf + Cm = 100. Thus, we can express Cf as Cf = 100 - Cm. Substituting this into Equation III gives us 3Cm = 100 - Cm, leading to 4Cm = 100 and consequently, Cm = 25.
This allows us to calculate Pf: Pf = 120 - Cm = 120 – 25 = 95. Therefore, T can be determined as T = Pf + 160 = 95 + 160 = 255.
We have successfully solved the puzzle!
The first video titled "How to Solve a Logic Puzzle" offers an insightful overview of similar problem-solving techniques, providing additional strategies to enhance your skills.
Chapter 2: Exploring More Logic Challenges
To further test your logic skills, check out this viral logic test from Cambridge.
This second video titled "Viral Logic Test from Cambridge" presents an engaging challenge that encourages critical thinking and problem-solving in a fun way.
If you enjoy these puzzles and would like to support more content like this, consider contributing on Patreon!