Problematics | Wordle deduction with Scrabble tiles - Hindustan Times

Problematics | Wordle deduction with Scrabble tiles

Oct 23, 2023 02:02 PM IST

Try this game of deduction in which three persons know a letter each. What is the word that can be formed with these three letters?

Having had World Cup puzzles for two consecutive weeks to set the event on its way, it makes sense to move on to something else now. Something new. Although Problematics is over 60 weeks old, there are still some categories of puzzles that we haven’t had even once so far.

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

For example, there are puzzles about some people who always tell the truth and some who always lie, and you have to determine the answer to certain questions based on their responses to the same or other questions. That kind of puzzle must make its debut here in the future.

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Another category involves a set of very intelligent people who are asked to solve a puzzle, and each one cracks it based on what the others before them have said. Here’s the first of those puzzles:

#Puzzle 61.1
#Puzzle 61.1

#Puzzle 61.1

Three bright young people once urged me to give them a puzzle. “Read Problematics,” I advised them, but they chorused in reply: “Solved those already. Give us something new.”

Thus cornered, I took out a Scrabble board and scattered the tiles across it. Asking them to shut their eyes, I handed each of them a different tile and hid away the rest.

“Open your eyes and look at your own tiles,” I told them, “but don’t show them to one another.”

I then displayed a sheet of paper, on which were written the following five words:


“One of these words can be formed by the three letters you hold,” I told them. “How many of you know what that word is?”

Youngster #1 was the first to reply: “I know.”

Youngster #2: “I know now.”

Youngster #3: “I know too, thanks to the replies by Youngsters #1 and #2.”

Who held which letter, and how did each of them reason it out?

Puzzle 61.1
Puzzle 61.1

#Puzzle 61.2

In a school where each class has between 20 and 30 students, several students in one class scored 100 out of 100 in mathematics. If you pick any two students from that class at random, the probability that both scored 100 is exactly 50%.

What is the number of students, and how many aced the paper?

Mailbox: Last week’s solvers

#Puzzle 60.1

Hi Kabir,

Let us divide the teams into two sets: Set 1 consisting of Netherlands, Bangladesh, Sri Lanka, Afghanistan and England, each with 7 wins, and Set 2 consisting of New Zealand, India, Pakistan, Australia and South Africa, each with 4 or fewer wins.

In Set 2, SA lost against all others; Australia won only against SA; Pakistan won only against Australia and SA; India won only against Pakistan, Australia and SA; NZ won against India, Pakistan, Australia and SA.

Each team in Set 1 won against each of the 5 teams of Set 2, plus against 2 teams from Set 1. Intra Set 1 results were:

  • The Netherlands defeated Sri Lanka and England.
  • Bangladesh defeated the Netherlands and Afghanistan.
  • Sri Lanka defeated Bangladesh and Afghanistan.
  • Afghanistan defeated the Netherlands and England.
  • England defeated Bangladesh and Sri Lanka.

— Prof Anshul Kumar, Delhi

#Puzzle 60.2

Hi Kabir,

If I accept the bet, only you can gain 100 by losing the bet. In either case, I’ll not gain anything.

If you win the bet, then none of us will gain anything. In this case, I’ll give you 200, and you’ll give me 300 back. You’ll win and I’ll give you another 100 for winning the bet.

If you lose the bet, you’ll still gain. Here, I’ll give you 200 and you’ll not return me anything. You lose the bet and will give me 100. So, you gain 100.

— Rachna Jain, Delhi

Solved both puzzles: Prof Anshul Kumar, Rachna Jain, Ar Kamal Passi, Amit Khanna, Bhasker Mundra, Rajesh Bansal, Dr Nakul Makkar, Adeep Atey, Gp Capt RK Shrivastava (retd), Shawn Jacob, Akshay Bakhai, Kanwarjit Singh, Vineet Kumar Dargan, Musarrat Rai Handa, Harsh Ozare

Solved #Puzzle 60.1: Kaustav Goel, Charvi Brajpuriya, Ananya Arvind, Prof Rosy Ahluwalia, Dr GL Arora, Major Jaideep, Ravinder Gahlout, Abhishek Garg, Anil Khanna, Arun Kumar Gupta, Raghav Kapre, Sabornee Jana, Dhruv Kundrai, Ajay Ashok, Asif Akbarali Karmali, Shishir Gupta, G Arvind, Bhuvi Jain, Narendra Prasad, Rahul RB

Solved #Puzzle 60.2: Nathan Sequeira, Dr Sunita Gupta, Mayobhav Pathak, Yadvendra Somra, Anil Kashyap, Amardeep Singh, Ranjan Ghosh

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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