Problematics: Class of equationshttps://indianexpress.com/article/blogs/problematics-class-of-equations/

Problematics: Class of equations

In this week's Problematics, the examination season has given us some puzzling inspiration.

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In this week’s Problematics, the examination season has given us some puzzling inspiration.

There goes the World Cup, which fed “Problematics” continuously with cricket puzzles. Following the news cycle, let’s now turn to the examination season for puzzling inspiration.

A school has 1,700 students in just two classes, IX and X. The student-to-teacher ratio is ideal, the facilities are fabulous and the students, as you might have guessed, are exceptional. The students in Class IX outnumber those in X.

In the Class X finals just ended, every student is going to score full marks in two subjects out of five. Peeking into the future, we find that all the boys and all the girls have got this perfect score in Social Science. The other such subject varies from student to student.

From this feel-good narrative we must now take a plot twist. Here comes my horror story, built loosely around an idea I borrowed from Archimedes.

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1) The number of boys with full marks in Maths is equal to 2/5ths of the boys with 100% in English plus the entire set of boys with a perfect score in Science.

2) The number of boys with full marks in English is equal to 1/4th of the boys with 100% in Hindi plus all the boys with a perfect score in Science.

3) The number of boys with full marks in Hindi is equal to 1/5th of the boys with 100% in Maths plus all the boys with a perfect score in Science. If the boys didn’t scare you, wait until you meet the girls.

4) The number of girls with full marks in Maths is equal to 2/5ths of all the students (girls and boys) with 100% in English.

5) The number of girls with full marks in English is equal to 1/5th of all the students with a perfect score in Hindi.

6) The number of girls with full marks in Hindi is equal to 1/4th of all the students with 100% in Science.

7) The number of girls with full marks in Science is equal to 5/12ths of all the students with a perfect score in Maths.

Puzzle#4A: Eight unknowns, seven equations, one puzzle — subject by subject, how many boys and girls scored full marks in which?

What you wrote

Last week’s puzzles were probably easier than usual. Here are your answers.

 Kabir, I really love your posts. Been solving puzzles after many years. In Puzzle#3A, to make sure we get the same amount of money, we need to ensure winning amount is equal whether India/Australia/NZ wins.

prob

Total 47

This way, total investment = 47 + 8 (entry fee)
Winnings = 60
Profit = 5
The assumption here is that the entry fee is paid just once and not for every single bet.

— M Natrajan (Class of 2009, IIM Calcutta)

Shalesh Kumar, Tushar Gupta and Sampath Kumar V are the others who have come up with the same answer.

Kabir, The answer to your Puzzle#3B is SMRITI IRANI
Cabinet minister with six letters from “MINISTER” = SMRITI
Surname of same minister from “A MINISTER” = IRANI

— Anil Kumar Agrawat

That one got over a dozen correct answers. Thanks for writing, Alex Anthony, Lakshmi Swathi Gandham, Vivek Anjan, Sanjeev Agrawal, Surya Ramanayam, Nalin Tikoo, Tariq Ayoob Mattoo, Dhiraj Jain and Harit Patel. “Problematics” regulars Anil Kumar, Sampath Kumar V, M Natarajan and Tushar Gupta complete the list.

Puzzle#4B: The last word

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If A = 1, B = 2 and so on until Z = 26, and if the “value” of any word is the product of its “letter-values” (eg. CAT = 3 × 1 × 20 = 60), then what is the highest value you can manage from a word of three letters? This is a contest, so send in your best effort, one word from every reader who feels up to it. The highest scorer wins.

Please mail your replies to: kabir.firaque@expressindia.com