Monday, April 13th, 2020
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
Actor | Average weekly collection (in Cr) |
Arshad | 36 |
Bhumi | 28 |
Chunky | 43 |
Danny | 34 |
Esha | 24 |
It is also known that,
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?
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.
No.of Weeks/Movie | A(Arshad) | B(Bhumi) | C(Chunky) | D(danny) | E(Esha) |
Avg | 36 | 28 | 43 | 34 | 24 |
4 | 144 | 112 | 172 | 136 | 96 |
5 | 180 | 140 | 215 | 170 | 120 |
6 | 216 | 168 | 258 | 204 | 144 |
7 | 252 | 196 | 301 | 238 | 168 |
8 | 288 | 224 | 344 | 272 | 192 |
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 3rd 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.
No.of Weeks/Movie | A(Arshad) | B(Bhumi) | C(Chunky) | D(danny) | E(Esha) |
Avg | 36 | 28 | 43 | 34 | 24 |
4 | 144 | 112 | 172 | 136 | 96 |
5 | 180 | 140 | 215 | 170 | 120 |
6 | 216 | 168 | 258 | 204 | 144 |
7 | 252 | 196 | 301 | 238 | 168 |
8 | 288 | 224 | 344 | 272 | 192 |
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.
No.of Weeks/Movie | A(Arshad) | B(Bhumi) | C(Chunky) | D(danny) | E(Esha) |
Avg | 36 | 28 | 43 | 34 | 24 |
4 | 144 | 112 | 172 | 136 | 96 |
5 | 180 | 140 | 215 | 170 | 120 |
6 | 216 | 168 | 258 | 204 | 144 |
7 | 252 | 196 | 301 | 238 | 168 |
8 | 288 | 224 | 344 | 272 | 192 |
b) If M5 is Arshad (144) is lowest
No.of Weeks/Movie | A(Arshad) | B(Bhumi) | C(Chunky) | D(danny) | E(Esha) |
Avg | 36 | 28 | 43 | 34 | 24 |
4 | 144 | 112 | 172 | 136 | 96 |
5 | 180 | 140 | 215 | 170 | 120 |
6 | 216 | 168 | 258 | 204 | 144 |
7 | 252 | 196 | 301 | 238 | 168 |
8 | 288 | 224 | 344 | 272 | 192 |
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
Daryl Thomas – thomasdar*****@gmail.com
Name of the students who provided the right answer:
Abhinaba paul choudhury | abhina******@gmail.com |
Vishwajeet Kumar | vish******@gmail.com |
Sanket Sharma | sanketshar******@gmail.com |
Rohan Bhaskar | rohanbhask******@gmail.com |
Gautam Madaan | gautammad*****@gmail.com |
Garima Yadav | garimaya*****@yahoo.in |
Pranay Kothari | pranaykotha******@gmail.com |
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