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Puzzle of The Week – Best Solution Wins Cash Prize – Movies are a great leveler – Updated with Solution

Monday, April 13th, 2020

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Puzzle of The Week – Rules and Prize

• You need to email your solution before 12th April (Sunday midnight) to [email protected]  
• Best solution will be decided by our faculty team.
• Cash prize of Rs. 500 or free telephonic discussion with Ravi Handa sir about MBA Prep.
• Cash prize of Rs. 500 will be transferred to your PayTM wallet.
• Your solution will be published on the website with your name.
• A quiz is open to everyone above the age of 18.
• You will need to submit an identity proof in case you win a cash prize.

Puzzle of The Week – Question

Movies are a great leveler. Whether you are a billionaire or someone who works with his hands from 9 to 5 to make a living, we all enjoy a good story. It is often said that Shakespeare would have really loved cinema. After all, it is life at 24 frames per second. And in the honor of great cinema, our puzzle today is based on a cinematic theme. I have taken inspiration from real names, events, and characters to frame this puzzle. Hope you like it.

Twenty thousand people gathered for the International Filmfare awards at Bandra Kurla Complex, Mumbai. Arshad has won the award for Best Actor (male), Bhumi has won te award for the Best actor (female), Esha has won the award for the best new comer. Now, the next category is for the “Most Popular Bollywood movie” .

The Top 5 Bollywood Movies of 2019 featured exactly one of these actors in the lead role :

The person who has won the award for Best Actor ( male)

The person who has won the award for Best Actor (female)

Chunky, Danny, and the person who has won the best new comer.

Each of these movies was featured in the Multiplexes for distinct number of weeks where minimum duration is 4 weeks & maximum duration is 8 weeks. The average weekly collection of each of these five movies (in Cr) is tabulated below

It is also known that,

1. The total collection of movie in which Chunky acted was not the highest.
2. The total collection of each of the five movies was different.
3. The total collection of the movie in which Esha acted was not the least.
4. The total collection of the movie that had the highest revenue was at most two times the total collection of the movie whose collection was least.
5. The total collection of the movie in which Bhumi acted was the median of all the movies when they were arranged in either ascending or descending order.
6. The ratio of number of movies which were shown for lesser number of weeks to number of movies shown for more number of weeks that Bhumi’s movie was 3:1.

The jury wanted to give the “Filmfare Award for the most popular movie” to the movie with the highest total collection in 2019. Who starred in the movie that won the award?

Puzzle of The Week – Solution and Winner

The Answer is Arshad at 216 Crores.
Which movie was awarded the Filmfare Award for the most popular movie : The one starring Arshad

Solution :

1) There are 5 movies.

2)  Each movie is show for distinct number of weeks from 4 to 8 weeks.

Therefore 4,5,6,7,8 weeks need to be counted with one allocated to each movie.

Let the movie actor’s first letter represent the movie name. i.e. A for Arshad, B for Bhumi and so on. We will create a matrix calculating collections for each actor for 4 to 8 week range.

 

3) Chunky cannot be the highest. Thus collections of 301&344 are eliminated as they would not be matched by any other movie.

4) Each movie had a different collection.

5) Movie acted by Esha is not the least, thus 96 is eliminated, 120 is possible if bhumi is at 112.

6) Movie with the highest revenue was at most two times the lowest. Let us just remember this condition along with 4 for now.

7) Bhumi was the median in all movies, Thus in ascending or descending order Bhumi must be the 3^rd highest or lowest collection.

8) Number of movies shown for weeks less than bhumi to higher than Bhumi are 3:1, therefore 3 people below number of weeks of Bhumi’s movie, and one person’s movie above number of weeks of Bhumi’s movie. Since all were shown for a distinct number of weeks, we can assume Bhumi was shown for 7 weeks. i.e. 196 Cr collection.

Thus 3 movies will be show for 4,5 and 6 weeks.

1 movie for 8 weeks.

9) If the movies are in the order M1,M2,M3,M4,M5  from highest to lowest collection, since Bhumi is at 196 and the median we can assume the following order.

M1

M2

196

M4

M5

With the condition that, M1 <= 2M5

Since 196 by Bhumi is highlighted lets go back to the matrix.

 

Also since Bhumi cannot be 112, Esha cannot be lowest and thus 120 is struck out.

10) Now if 196 should be the median, 2 need to be more than 196 and 2 less than 196. The values that can be more are 288,216 from Arshad, 258,215 from Chunky,204,272 from Danny.

Now if the lowest possible is 136 by Danny, 2 times 136 is 272. Thus Arshad cannot be at 288.

Thus Highest can be Danny at 272, or Arshad at 216, in Which case Chunky cannot be at 258.

11) Thus M1 can be (272(Danny),216(Arshad))

M5 can be (136(Danny),144(Arshad),172(Chunky))

Let us eliminate the lowest possibilities.

a) If M5 is 172(Chunky), then one more M4 needs to be less than 196 i.e. either Danny at (170) or Arshad at (180) or Esha at (192).

If M4 – Danny(170), Arshad has to be 216, and Esha is left with 192, then Bhumi is not the median.

If M4 – Arshad(180), Then We can have two possibilities,

Dany (204) & Esha (192) -again Bhumi isn’t median

Or Danny (272) & Esha (192) again Bhumi isn’t median

If M4 is Esha(192)

M2 & M1 need to be above 196 for Danny and Arshad which is not possible, as

both are above 196 in the same week 6.

Chunky cannot be lowest at 172.

b) If M5 is Arshad (144) is lowest

M4 can be Chunky at 172, Esha at 144,192 and Danny at 136 or 170. But to get two values above 196, only chunky and Danny are possible, in which case highest will always be chunky which is against rule in step 3)

Thus Arshad cannot be lowest.

c) If M5 is Danny at 136

M4 can be Esha at 144,192 or Arshad at 180.

If Arshad is lowest at 180, again chunky will have to be highest.

If Esha is 144, again chunky will be left as highest.

If Esha is 192 at M4. We need M2 & M1 > 196

If Chunky is at M2 at 215 and Arshad is at M1 at 216

M1      216

M2      215

M3      196

M4      192

M5      136

No other possibilities exist and thus this is the only correct possibility.

This follows all rules.

Thus Arshad’s is the highest movie with 216 cr collection

 

Puzzle of The Week – Winner

Daryl Thomas – thomasdar*****@gmail.com

Name of the students who provided the right answer:

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