Problematics | Rubik’s colours and Pythagorean triples

Mar 15, 2023 10:12 AM IST

This week's puzzles include a mischievous child, a Rubik's cube, and the Pythagorean triangle. Good luck!

The Rubik’s Cube, invented in 1974, was a rage in the 1980s. For readers who were too young then, here’s a basic description.

Welcome to Problematics! (Shutterstock) PREMIUM
Welcome to Problematics! (Shutterstock)

It is made of 26 smaller cubes arranged in a 3 × 3 × 3 configuration (there’s no cube at the centre). Each of the six faces has its cubes in a 3 × 3 arrangement, so that what you see front-on is 9 squares per face, or a total of 54 squares that come in 6 different colours.

The idea is to keep rotating the cube’s 3 × 3 planes until you have the same colour on any one face (basic) or more faces, possibly all (advanced), but that is not the point of the puzzle below.

#Puzzle 29.1.
#Puzzle 29.1.

Puzzle 29.1: A mischievous child drops a Rubik’s Cube into a can of red paint, takes it out and waits for the paint to dry. Once every face is permanently red, the child smashes the toy into its 26 smaller cubical components. How many of these cubes have (i) one red face, (ii) two red faces and (iii) three red faces?

#Puzzle 29.2.
#Puzzle 29.2.


Solving #Puzzle 28.1.
Solving #Puzzle 28.1.
#Puzzle 28.2:

Hi Kabir, 

The four capitals in the anagram are:  AMSTERDAM, BERLIN, LISBON, TEHRAN 

— Mudit Singhal, Mumbai 

Solved both puzzles: Sanjay Gupta (Delhi), Mudit Singhal (Mumbai), Prisha Gupta (Amity International School, Saket, Delhi), Col Amol Gill (Gangtok), Dhairyan Jain (Mumbai), Jasleen Kaur (Delhi), Ojasvi Jain (Delhi), Rutu Milind Save (Mumbai), Mayobhav Pathak (Gurgaon), Raghav Kapre, Raju Ramalingam (Bangalore), Sarang Sule (Mumbai), Aurelia Lopez (Vasai), Ihit Bhardwaj (Navi Mumbai), Biren Parmar (Bay Area, California), Rahul Agarwal (Bay Area, California), Md Aqueel Iqbal (Hansraj College, Delhi), Bhavya SK & Dr Vivek CK (Delhi), Sabornee Jana (Mumbai), Vinod Mahajan (Delhi), Geetansha Gera (Faridabad), Dr Gurbachan Arora (Delhi), Dr Vivek Jain (Baroda), Shishir Gupta (Indore), Jyoti Bhat (Mumbai), Dr Nakul Makkar (Noida), Jasvinder Singh (Nabha), Sunita & Naresh Dhillon (Gurgaon), Samarth Dewan (Panchkula) 
Solved #Puzzle 28.1: Bhavishya (Panchkula), Ayush Bhatt (Delhi), Aadya Sinha (Delhi), Kushagra K (Noida), Ajay Kumar (Patiala), Nupur Bharara, Rajesh Haridas Asher, Sunita Gupta (Delhi), Aaditya Bhatia (Faridabad), Ashish Sethi, Nikunj Kumar 
Solved #Puzzle 28.2: Dhanya Sangwan (Delhi), Nishan Shetty (Thane), Swati Tandon (Delhi), Nathan Sequeira (Mumbai), Deviprasad Saksaria (Navi Mumbai), Ipsa Singh (Vaishali), Jaikumar Inder Bhatia (Ulhasnagar, Thane) 
#Puzzle 27.2.
#Puzzle 27.2.
Solved #Puzzle 27.2: Jasvinder Singh (Nabha), Arsh Gupta (Gurgaon), Sunita Gupta, Sandeep Kumar (Chandigarh), Rutu M Save (Mumbai), Mohit Kumar (Noida), Sanjiv, Himanshu Jain, Dr Nakul Makkar (Noida), Y K Munjal (Delhi), Dr Vivek Jain (Baroda), Tejpal Singh, Sunita & Naresh Dhillon (Gurgaon), Amar Lal Miglani (Mohali), Amardeep Singh (Meerut), Mudit Singhal (Mumbai), Rajender Parsad Agarwal (Delhi), Sarang Sule (Mumbai), Rahul Agarwal (Bay Area, Califiornia), Musarrat Rai Handa (Faridabad), Nathan Sequeira (Lakshdham High School, Mumbai), Rajesh Bansal (Noida), Harshit Arora (Delhi), Deviprasad Saksaria (Navi Mumbai) 
Apologies to Nipun Bamania for missing his name among the acknowledgements last week.

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

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    Puzzles Editor Kabir Firaque is the author of the weekly column Problematics. A journalist for three decades, he also writes about science and mathematics.

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