Problematics | Meet Gabbar Singh, probability theorist

How likely are Gabbar Singh's men to survive his partly loaded revolver? A mathematical perspective

The big moment has finally come. Among all the puzzles I have created, this is the one that has satisfied me the most. I held it back for a special occasion, and the 50th week of Problematics is as good an occasion as any. Besides, it’s topical: it’s based on Sholay, whose 48th anniversary is next week.

Welcome to Problematics!(Shutterstock)

You might be interested to know that the first time this puzzle appeared was in this very newspaper. That was in 2002, in the Kolkata edition of Hindustan Times. In 2015, I ran it online elsewhere. Now, it returns to the newspaper that first published it:

#Puzzle 50.1

#Puzzle 50.1

One of the most memorable sequences in Sholay is when Gabbar Singh confronts and punishes his three henchmen who have returned empty-handed from the nearby village, sent packing by two hired mercenaries. Let's review all that from a mathematical perspective

Gabbar takes a fully loaded six-shooter, fires three consecutive shots into the air, and spins the cylinder so that no one knows which three chambers are loaded and which three are empty. He presses the revolver to the temple of one of the offenders and prepares to shoot.

(a) What is the target's probability of surviving?

An empty click, Lucky man! Gabbar proceeds to the next man and prepares to shoot.

(b) What is the second man's probability of surviving?

Another lucky fellow! Over to the third man, same routine.

(c) What is his probability of surviving?

The third one too survives. You know how it goes from here, there's no puzzle about that.

#Puzzle 50.2

Here's an alternative scenario. Suppose, in the beginning. Gabbar fires a shot in the air, randomly rotates the cylinder, fires a second shot, coincidentally expending a bullet, rotates the cylinder and fires a third time, expending a third bullet. Now, after rotating the cylinder again, he repeats the exercise described in #Puzzle 50.1.

Find the probability of each man's survival before each shot is fired, and after the previous man has survived.

MAILBOX: LAST WEEK'S SOLVERS

#Puzzle 49.1

#Puzzle 49.2

Hi Kabir "You can't eat your cake and have it too." This should be the modem-day version.

-Madhuri Patwardhan, Thane

Many readers have offered the alternative. “You can't have your cake and eat it too.” Both versions are acceptable as solutions, although “eat your cake and have it too” fits the mother's words better.

What's nice is that some school kids have solved the second puzzle. Kanica Gupta of Ghaziabad is 8 years old Charvi Brajpuriya and Arhat Brajpuriya of Faridabad are 11 and 11 respectively.

Solved both puzzles: Prof Anshul Kumar (Delhi), Madhuri Patwardhan (Thane), Dr Sunita Gupta (Delhi), Dr Nakul Makkar (Noida), Shawn Jacob (Navi Mumbai), Harshit Arora (Delhi), Akshay Bakhai (Mumbai), Kanwarjit Singh (Delhi, Sunita & Naresh Dhillon (Gurgaon), Joydeep Mahato (Delhi), Beauty Mahato (Delhi), R Parakh, Sanjana Rane

Solved #Puzzle 49.1: Arzoo Gera (Faridabad), Saurabh Bansal

Solved #Puzzle 49.2: Kanira Gupta, Charvi Brajpuriya & Arhat Brajpuriya, Carol Miranda, Dr G L Arora, Ashim Goswami, Sandeep Bhateja, Amardeep Singh, Aarika, Namrata Ghosh, Nipun Bamania, Avni Nayak, Savleen Kaur

Arora, Vikas Nanda, Nathan Sequeira, Anil Goyal, Rozina Sehgal, YK Munjal, Deviprakash Seksaria, Shri Ram Aggarwal, JL Aggarwal, Vivek Aggarwal, Sankaran KB, Geetansha Gera, A Chowdhury, Suryakant Bhogle, Swati Gupta

Problematics will be back next week. Please send in your replies by Friday noon to problematics@hindustantimes.com