Problematics | The weight of a bulldog and friends

Nov 07, 2022 02:27 PM IST

The following kind of puzzle is one involving two equations and three variables, whose values you need not determine while getting to the answers you are looking for.

Back in school, your mathematics teacher will have told you that for any system of equations to have a unique set of solutions, the number of equations must be equal to the number of variables. While that is true, the fun fact is that we can still solve puzzles that involve fewer equations than variables.

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

Given certain terms and conditions, it is possible to solve a single equation in two variables, as you showed a couple of months ago when you solved #Puzzle 3.1. And then there is the following kind of puzzle, this one involving two equations and three variables, whose values you need not determine while getting to the answers you are looking for.

#Puzzle 11.1
#Puzzle 11.1
#Puzzle 11.1 and #Puzzle 11.2
#Puzzle 11.1 and #Puzzle 11.2
Mailbox: Last week’s solvers 

Puzzle #10.1

Hi Kabir,

The escalator has 48 steps when it's still, and you walked 24 steps on your way up.

Let the number of steps when the escalator is still be n; and the speed of the escalator be s steps/second.

The speed of the woman, who is twice as fast as you = 2 steps/sec. Distance = 32 steps; time = 16 seconds.

n – 16s = 32

Speed of the child = 3 steps/sec. Distance = 72 steps; time= 24 secs.

n + 24s = 72

Solving, n= 48 steps, s = 1 step/sec

Now, let the number of steps you take be t. Your speed = 1 step/sec; time taken = t seconds.,

48 – 1t = t

Or, t = 24 steps.

— Anushka Rai, Motilal Nehru College, DU

#Puzzle 10.2

Hi Kabir,

This puzzle will have an “out of the box” answer.

If one of them is not a 5 note, but the other is (trick question) — so, one 50 note & one 5 note.

— Madhuri Patwardhan, Thane

Solved both puzzles: Prakash Bhate (Mumbai), Avneesh Tomar (Delhi), Gopal Menon (Mumbai), Anushka Rai (Motilal Nehru College, DU), Sanidhya Saumay (Mumbai), Shawn Jacob (Mumbai), Manthan Dhabriya (Mumbai), Aarti Pandey (Noida), Natrajan (Bangalore), Shishir Gupta (Indore), Col (Dr) J S Sabharwal (Mohali), Madhuri Patwardhan (Thane), Yojit Manral (Faridabad), Sandeep Bhateja (Hoshiarpur), Jasvinder Singh (Nabha), Geetansha Gera (Faridabad) 
Solved #Puzzle 10.1: Gauri Mudgal, Vinod Mahajan (Delhi)
Solved #Puzzle 10.2: Raunaq Nayar (Delhi), Surendra Mehta (Noida), Nipun Sharma (Delhi), Ajay Ashok (Mumbai), Amarjeet Singh (Meerut), Biren Parmar (Bay Area, California), Ravinder Gahlout (Gurgaon)

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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