Code360 powered by Coding Ninjas X Naukri.com. Code360 powered by Coding Ninjas X Naukri.com
Table of contents
1.
Introduction
2.
Problem Statement
3.
Solution
4.
Frequently Asked Questions
4.1.
What is a puzzle?
4.2.
What are the advantages of solving puzzles?
4.3.
How to solve a direction-based puzzle?
4.4.
How many points of solution will be there if, instead of the east, you turn to west from point B?
4.5.
How many points will there be in the globe if we move one mile north from point A, then move one mile east and move one mile south, then you will reach back at point A.
5.
Conclusion
Last Updated: Mar 27, 2024

One Mile on the Globe

Author Aditya Singh
0 upvote
Master Python: Predicting weather forecasts
Speaker
Ashwin Goyal
Product Manager @
Interview Puzzles

Introduction

Puzzles are good exercise for the brain. They help in enhancing the cognitive abilities of the brain helping with Problem Solving and related skills. There are numerous types of puzzles; each one having a logic inherent to itself which helps in cracking it. A good puzzle well is actually like a good mystery that we may have read about or watched on TV. It has the finest of hints which help in reaching its solution.

The following article discusses one such puzzle so let's get right to it.

Problem Statement

How many points are there on the globe where you reach the place where you started by walking one mile south, one mile east, and then one mile north?

  • Case 1: The Answer is a function of N. Output it with N with multipliers or divisor numbers following N. For example, N / 2, N * 3 / 4.
  • Case 2: The answer is an integer. Just put the number without any decimal place if it's an integer. Suppose the answer is Infinity, output Infinity.
  • Case 3: Floating number. Round it off to two decimal places & output it as I.xx, where “I” is the integer part of the answer, & xx are two decimal digits after rounding off.
Get the tech career you deserve, faster!
Connect with our expert counsellors to understand how to hack your way to success
User rating 4.7/5
1:1 doubt support
95% placement record
Akash Pal
Senior Software Engineer
326% Hike After Job Bootcamp
Himanshu Gusain
Programmer Analyst
32 LPA After Job Bootcamp
After Job
Bootcamp

Solution

There would be infinite numbers of solutions for the above problem. Let’s see how:

illustration image

Firstly, the north pole is one of the answers because moving one mile south from the north pole and then moving one mile to the east takes you to the latitude of the globe, and then moving one mile north takes you back to the north pole. Hence the North Pole is one of the solutions.    

Now, consider the points 1 + 1/(2*π) miles away from the south pole; let's take one of these points as point A. Then go one mile south to point B. Then when you go one mile east from point B, you will come back to point B by traveling through each line of longitude. Then moving a mile north takes you back to point A. 

There are also points closer to the south pole such that moving a mile east brings you back to point B passing through each longitudinal line exactly twice, thrice, or many more times as you want. Hence, there are an infinite number of these concentric rings, and in these rings, there are an infinite number of points.

Therefore, from the above explanation, we can say that there are an infinite number of points on the globe.

Check out this problem - 8 Queens Problem

Frequently Asked Questions

What is a puzzle?

A puzzle is a game of words, toys, questions, etc., that helps in increasing our problem-solving ability.

What are the advantages of solving puzzles?

Solving puzzles enhances the problem-solving skills of a person. It also improves the logic building of a person.

How to solve a direction-based puzzle?

For solving a direction-based puzzle question, first draw the four directions north, east-west, and south. Then imagine the movements in the real world and imagine the shape of the world or globe while solving. 

How many points of solution will be there if, instead of the east, you turn to west from point B?

If we move west from point B instead of the east, there will be infinite points on the globe because the earth is round in shape. Hence, moving west will not change the answer. 

How many points will there be in the globe if we move one mile north from point A, then move one mile east and move one mile south, then you will reach back at point A.

One of the answers will be the south pole. And the remaining answers are at a point 1 + 1/(2*π) miles away from the north pole on the latitudinal axis of the globe. Hence, there will be infinite points in the world.

Conclusion

In this article, we discussed the ‘One Mile of the Glode’ puzzle. This puzzle is based on finding the number of points present in the globe by following the respective given directions mentioned in the question.

Recommended Readings:


Do check out The Interview guide for Product Based Companies as well as some of the Popular Interview Problems from Top companies like Amazon, Adobe, Google, etc. on Coding Ninjas Studio.

Also check out some of the Guided Paths on topics such as Data Structure and Algorithms, Competitive Programming, Operating Systems, Computer Networks, etc. as well as some Contests, Test Series, Interview Bundles, and some Interview Experiences curated by top Industry Experts only on Coding Ninjas Studio.

Happy Learning!

Previous article
Next Number
Next article
Marbles in the Jar
Live masterclass