Problematics | Births and dates with new puzzles

Sep 12, 2022 12:08 PM IST

We are familiar with mathematical tricks in which you think of a number and I tell you what it is. In this variation, let’s use dates instead of numbers.

PUZZLE 3.1 AND 3.2

We are familiar with mathematical tricks in which you think of a number and I tell you what it is. In this variation, let’s use dates instead of numbers. Ask a friend to multiply her birth date by 12, and her birth month (Jan = 1, Feb = 2, etc) by 31. She adds the two products and tells you the sum, and you surprise her by announcing her birthday.

For example, if she tells you the sum is 357, you declare: “Your birthday is March 22” (12 × 22 + 31 × 3 = 357).

How did you work it out? You began with a single equation in the variables d (date) and m (month): 12d + 31m = 357

One equation with two variables can have infinitely many solutions, but not if you factor in the constraints: both variables are positive integers, d is not greater than 31, and m not greater than 12. Within those constraints, tinkering around with the equation and making smart observations will yield a unique solution.

The Russian writer Yakov Perelman discusses a generic solution to the equation in his popular book, Mathematics Can Be Fun. The example above is my own, as is the puzzle below.

Puzzle 3.1 and 3.2. 
Puzzle 3.1 and 3.2. 

#Puzzle 2.1  

Well... hopefully my answer is right. It is:   

Ashima — Delhi, Bankim — Chandigarh, Chand — West Bengal, Dilbar — Assam   

— Avani Gupta, Class 8th, Kulachi Hansraj Model School, New Delhi 

Solved #Puzzle 2.1:  Solved Puzzle 2.1: Natrajan (Bangalore), Ashwani Koul (Faridabad), Iram Kazi (Mumbai), Biren Parmar (Bay Area, California), Arun K Rao (Lucknow), Col (retd) J S Sabharwal (Mohali), Nupur Joshi (Delhi), Adwita (Mumbai), Charu Sharma (Delhi), Vineet Jain (Gurgaon), Gopal Menon (Mumbai), Priyanka Gupta (Delhi), Pranav Vashistha, Bhavna Kohli (Mumbai), Akshit Goel (Delhi), Sandra Danisha (Mumbai), Divya Prakash (Delhi), Priji Nair, Shailesh Poria (Mumbai), Krisha Choksi (Mumbai), Joy Pandya (Mumbai), Vinay Shrivastav, Aditya Mazumdar (Greater Noida), Aryaveer Singh (Delhi), Archit Kapur (Delhi), Ashish Prajapati (Chandigarh), Rakshit Jain (Ghaziabad), Sudesh Chand Dogra (Delhi), Dev Pandit (Mumbai), Kshitij Kumar (Sri Venkateswara College, New Delhi), Arpita Mary Abraham (Faridabad), Swati Chauhan (Delhi), Onkar Singh (Delhi), Radhika Gupta (Delhi), Sehejpreet Kaur (Delhi), Rihanna Naik (Navi Mumbai), Col (retd) Bharat Jhingon (Pune), Jasleen Kaur (Delhi), Caroline D’Cruz (Mumbai), Tarini and Riyash (Haryana), Musarrat Rai Handa, Devdas Thakuria (Gurgaon), Dr Neetu Jain, Vikrant Bhat (Delhi), Adeep Atey (Kalyan, Thane), Stuti Patwardhan (AIESEC in Mumbai), Arun Prajapati (Delhi), Dr Kamlesh Kumar Kanodia (Delhi), Avidha Sharma (Jalandhar), Purnima Wanchoo (Gurgaon), Disha Zaveri (Mumbai), K S Sridhar
Puzzle 2.2
Puzzle 2.2
#Puzzle 2.2 strategies: Natrajan suggests PLANK followed by CLOVE, if necessary. For Nupur Joshi, it’s SCRAP followed by KNAVE. Iram Kazi, Arun K Rao, Biren Parmar, Vineet Jain and Yogita Jamwal (Delhi), writing separately, would go for PLUCK at move number 3. Ashwani Koul would go for CLAMP, and Col J S Sabharwal for either PLUCK or CLUMP. Not listing those who have tried to guess the word at the third move itself, which is weak strategy.  

Problematics will be back next week. Please send in your replies 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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