Problematics | When MI fans met Barbenheimer
Who is watching Barbie, Oppenheimer or MI-7? Who's the Nolan fan and who likes Tom Cruise?
In the hype around Barbie and Oppenheimer, which released on the same date, a third big-ticket film that got somewhat overshadowed was Mission Impossible: Dead Reckoning Part One. This instalment in the MI series had released just over a week previously, but ultimately Barbenheimer ruled.
Those who have watched all three movies, or want to, will have their own ideas about which is the best order to do so. Meet the following group of friends, who differ in their choices.
On a Sunday, these eight friends watch one movie each among Barbie, Oppenheimer, and MI7. To protect their identities, let’s call them Einsteinium, Lawrencium, Bohrium, Fermium (these four may or may not be watching Oppenheimer), Nobelium, Mendelevium, Curium and Rutherfordium.
One of the eight is a fan of Oppenheimer director Christopher Nolan, while the seven others have a favourite actor each from among the stars of the three films: Margot Robbie, Ryan Gosling, Cillian Murphy, Emily Blunt, Robert Downey Jr, Tom Cruise and Rebecca Ferguson. The movie anyone watches, however, may or may not be the work of his or her favourite star or director.
* Not more than three of the eight watch the same movie.
* Mendelevium avoids Oppenheimer because he does not like Downey Jr
* The Murphy fan and the Downey Jr fan miss Oppenheimer tickets and join the Ferguson fan in watching Mission Impossible
* Nobelium, who does not like MI7 stars Ferguson and Cruise, watches Oppenheimer instead
* But Curium, who likes Blunt, does not watch MI7
* The Cruise fan, on the other hand, watches Oppenheimer
* Lawrencium, who is a fan of Robbie, takes Fermium along to see Barbie
* Einsteinium and Rutherfordium go together to watch a movie, which is not what Nobelium is watching
* Neither Mendelium nor Rutherfordium is particularly fond of Ferguson
* The Gosling fan watches Barbie, of course
Who is watching what, and who is the favourite star or director of each?
Can you find the largest multiple of 11 that consists of 9 digits, all different?
Mailbox: Last week’s solvers
Yes, she can do it in just two weighings.
In the first weighing, measure one bronze (B₁) and one silver (S₁) against the other bronze (B₂) + one gold (G₁). If they are equal, then S₁, B₂, G₂ must all have the same weight and S₂, B₁, G₁ must belong to the other set. The second weighing of any medal from the first group against any medal from the second group will determine which set is heavier.
If they are not equal in the first weighing, say if B₁ + S₁ is heavier, then B₁ is definitely the heavier of the bronze medals. But we don't necessarily know whether S₁ is the heavier silver; it could be that both S₁ and G₁ are from the lighter group.
For the second weighing, we measure B₁ + B₂ against S₁ + G₁. If S₁ + G₁ is heavier, then both of them must be from the heavier group. If S₁ + G₁ is lighter, then both are from the lighter group. If both sides are equal, then we can infer from the first weighing that G₁ is the lighter gold medal and S₁ is the heavier silver medal.
If in the first weighing, B₁ + S₁ was lighter, then we follow the mirror image of the above working.
— Ajay Ashok, Mumbai
The password is 9841.
— Akshay Bakhai, Mumbai
Solved both puzzles: Ajay Ashok (Mumbai), Akshai Bakhai (Mumbai), Prof Anshul Kumar (Delhi). Many others have attempted both puzzles, but the procedures they describe for #Puzzle 51.1 may require a third weighing at some stage or the other.
Solved #Puzzle 51.2: Vansh Srivastava, Vivek Aggarwal, William Feasey, Harshit Arora, Parth Gupta, Dushyant Goyal, Ankush Goyal, Dr Sunita Gupta, Aarika Goel, Aarush Singhal, Tirush Jindal, Parichit, Nipun Bamania, Harsh Ozare, Yadvendra Somra, Shivika Gupta, Vikas Nanda, Shruti M Sethi, Avanti Kashikar, Mayobhav Pathak, Dhruv Singla, Anil Khanna, Bimal D Jhaveri, Adeep Atey, Deviprakash Seksaria, Dhruv Kundrai, Kanwarjit Singh, Nathan Sequeira, Rajesh Bansal, Vinod Mahajan, Akshaya Paul, Amardeep Singh, Sunita & Naresh Dhillon, Shishir Gupta, Anay Gupta, Shri Ram Aggarwal, Dr Vaibhav Aggarwal, Madhuri Patwardhan, Jawahar Aggarwal, BS Sharma, Rishi Singh, Sunitha Nair
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