Problematics | How to win at Scrabble

As longtime readers of Problematics know, I frequently create puzzles of my own but also pick up existing ones and adapt them. Occasionally, some puzzles are so original that they cannot be adapted, so I reproduce those without making changes and credit their creator wherever their name is known.

But where do those existing puzzles come from? Over a lifetime, I have collected dozens and dozens of books, some of them dealing exclusively with puzzles, and others dealing with subjects from which I can create my own puzzles, such as word games, card games, magic tricks and even popular science publications.

Among these hundreds of puzzles and puzzle ideas, one had slipped me all these decades before I came across it last week. Duly modified for HT readers, it is the first of the two puzzles that appear below. The second puzzle is entirely my own.

#Puzzle 84.1

Victor and his wife, Victoria, sit down to a contest in Scrabble. To keep it exciting, they decide to play for stakes. Not that it matters who wins and who loses: They figure that the money will remain in the family either way.

“How much do we play for?”

“It’s boring to play for the same amount every game,” Victoria replies. “So, let’s keep doubling the stakes in successive games.”

Victor: And we start with…?

Victoria: ₹1 in the first game. Then ₹2 in the second game, ₹4 in the third, and so on.

Victor: Powers of 2 mean that the stakes can jump very quickly. If you are going to win, I will play until I lose ₹500, and no further.

His premonition proves correct: His wife is the eventual winner. After a certain number of games, Victor crosses the limit he has set for himself.

“Here’s your ₹500,” he tells her, handing her a note fresh from the ATM.

“You still owe me ₹1, though,” Victoria replies.

How many games did they play, and who won which games?

#Puzzle 84.2

News of the Victor/Victoria contest described above eventually reached the cricketing world. During a break in a T20 tournament that is played on the lines of the IPL, the captains of Eastern Riders, Western Indians and Southern Kings compare their performances using the Scrabble contest for reference.

Edited excerpts from their conversation:

ER Captain: Since we like puzzles, let’s take the cue from Victor and Victoria. I start with my total in the tournament so far, keeping it as is.

WI captain: I double my total.

SK captain: And I multiply mine by 4.

Chorus: Our grand total becomes 911.

ER Captain: Of course, I should have scored a lot more than I actually did. But for a couple of umpiring errors, I reckon my total would have been seven times what it actually is.

WI Captain: And my total would have been five times my actual total.

SK captain (modestly): I have no complaints; my total is exactly what it should be.

Chorus: In that scenario, our grand total would be 1,616.

What is the actual grand total of the three captains’ scores?

MAILBOX: LAST WEEK’S SOLVERS

#Puzzle 83.1

Hi Kabir,

The magician identifies the colours taken by the 3 Idiots based on the number of sweets remaining in the box. My solution is summarised in the table as shown.

— Anil Khanna, Ghaziabad

#Puzzle 83.2

Hello Kabir,

The hidden word in the Wordle puzzle is HYPER.

— Sanjay S, Coimbatore

Two solvers have made some calculation mistakes with the first puzzle. I am, however, listing them as correct because they have otherwise proceeded with the right approach.

Solved both puzzles: Anil Khanna (Ghaziabad), Sanjay S (Coimbatore), Dr Sunita Gupta (Delhi), Yadvendra Somra (Sonipat), Akshay Bakhai (Mumbai), Professor Anshul Kumar (Delhi), Sundarraj C (Bengaluru), Kanwarjit Singh (Chief Commissioner of Income Tax, retired), Aafiya (Coimbatore), YK Munjal (Delhi), Group Captain RK Shrivastava (retired, Delhi), Amarpreet (Delhi)

Solved #Puzzle 83.1: Dr Vivek Jain (Baroda), Ajay Ashok (Mumbai)

Solved #Puzzle 83.2: Jaikumar Inder Bhatia & Disha Bhatia (Ulhasnagar, Thane)

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