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September 21, 2020

How to Pursue Mathematics after High School?

For Students who are passionate for Mathematics and want to pursue it for higher studies in India and abroad.

Try this beautiful Geometry Problem based on a fly trapped inside cubical box from AMC 10 A, 2010. You may use sequential hints to solve the problem.

Fly trapped inside cubical box - AMC-10A, 2010- Problem 20

A fly trapped inside a cubical box with side length 1 meter decides to relieve its boredom by visiting each corner of the box. It will begin and end in the same corner and visit each of the other corners exactly once. To get from a corner to any other corner, it will either fly or crawl in a straight line. What is the maximum possible length, in meters, of its path?


  • $4+4 \sqrt{2}$
  • $2+4 \sqrt{2}+2 \sqrt{3}$
  • $2+3 \sqrt{2}+3 \sqrt{3}$
  • $4 \sqrt{2}+4 \sqrt{3}$
  • $3 \sqrt{2}+5 \sqrt{3}$

Key Concepts




Suggested Book | Source | Answer

Suggested Reading

Pre College Mathematics

Source of the problem

AMC-10A, 2010 Problem-20

Check the answer here, but try the problem first

$4 \sqrt{2}+4 \sqrt{3}$

Try with Hints

First Hint

Suppose the fly starts from the point \(A\).we have to find out  the maximum possible length. The maximum possible length will be from one corner to another corner such as .....

$A \rightarrow G \rightarrow B \rightarrow H \rightarrow C \rightarrow E \rightarrow D \rightarrow F \rightarrow A$

Now can you find out this maximum path?

Now can you finish the problem?

Second Hint

Given that the side length of the cube is $1$. Therefore the diagonal \(AC\)=\(\sqrt 2\) and the diagonal \(AG=\sqrt 3\). Now we have to find out the path \(AG+GB+BH+HC+CE+ED+DF+FA\).Can you find it ?

Now can you finish the problem?

Third Hint

\(AG+GB+BH+HC+CE+ED+DF+FA\)=\(\sqrt 3+\sqrt 2+\sqrt 3+\sqrt 2+\sqrt 3+\sqrt 2+\sqrt 3+\sqrt 2\)=(\(4\sqrt3+4\sqrt2\))

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What to do to shape your Career in Mathematics after 12th? 

From the video below, let's learn from Dr. Ashani Dasgupta (a Ph.D. in Mathematics from the University of Milwaukee-Wisconsin and Founder-Faculty of Cheenta) how you can shape your career in Mathematics and pursue it after 12th in India and Abroad. These are some of the key questions that we are discussing here:

  • What are some of the best colleges for Mathematics that you can aim to apply for after high school?
  • How can you strategically opt for less known colleges and prepare yourself for the best universities in India or Abroad for your Masters or Ph.D. Programs?
  • What are the best universities for MS, MMath, and Ph.D. Programs in India?
  • What topics in Mathematics are really needed to crack some great Masters or Ph.D. level entrances?
  • How can you pursue a Ph.D. in Mathematics outside India?
  • What are the 5 ways Cheenta can help you to pursue Higher Mathematics in India and abroad?

Want to Explore Advanced Mathematics at Cheenta?

Cheenta has taken an initiative of helping College and High School Passout Students with its "Open Seminars" and "Open for all Math Camps". These events are extremely useful for students who are really passionate for Mathematic and want to pursue their career in it.

To Explore and Experience Advanced Mathematics at Cheenta
Register here

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