Problematics | A gambler’s unlucky number - Hindustan Times
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Problematics | A gambler’s unlucky number

Nov 16, 2023 06:30 PM IST

Games of chance can be an endless source of puzzles. Here is a relatively simple one about a gambler for whom the number 37 appears to carry a jinx

Regular readers of Problematics, here’s an announcement: the way most of you access this column changes from today. All these months, the bulk of the responses to my puzzles came from readers of the print edition, outnumbering those who accessed my puzzles from the web version. From now on, at least for the foreseeable future, the web is the only place where Problematics will appear. It remains easy to access; all you need to do is use the Hindustan Times app on your mobile.

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

Nothing else changes. As always, here are two new puzzles for the week, followed by readers’ solutions to the previous week’s puzzles. At the same time, even though Problematics has been appearing simultaneously in print and online for nearly 15 months now, we can look at this as some kind of new beginning. This week’s puzzles, therefore, are deliberately kept a little easier than most previous ones.

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#Puzzle 64.1

The wife of a gambler secretly takes his debit card to an ATM and changes its PIN so that he can no longer withdraw more money than the family can afford to lose. To complete the lockout, she logs into his banking account and changes that password too.

The gambler, however, is more intrepid than his wife has bargained for. Finding his savings inaccessible, he breaks open his wife’s piggy bank and recovers a bunch of 10 coins — 64 of them. He goes to a gambling den that follows very simple rules: if a client places a bet on something, he either loses it all or wins that exact amount.

Years of losing have taught the gambler that one must never bet all their money at one time. He places 32 coins on the gambling table and keeps the remaining 32 as insurance for the future. And he wins! “Now I have 96 coins. I will bet half of those this time,” he decides and now places 48 coins on the table.

He wins again. Scarcely believing his luck, he counts his 144 coins and places 72 on the table, only to lose the third bet. Still optimistic, however, he stakes half his remaining coins and wins the fourth bet. Following the same strategy, he bets two more times, losing on both occasions.

Before going home, he counts his losses from the six bets: 32 + 48 – 72 + 36 – 54 – 27 = –37.

“I won three bets, lost three others, and was poorer by 37 coins in the end,” he thought. “If the same number of wins and losses had come in a different order, I might perhaps have made a profit.”

He calculated what might have happened if he had won the first three bets and lost the last three, and found that he would still have lost the same number of coins: 37. He looked at other combinations, but the end result was always the same.

Why does –37 keep coming up irrespective of the order of three wins and three losses?

#Puzzle 64.2

At a race in which the champion is 2.5 times as fast as the last-placed competitor, they finish six minutes apart. How much time did each of the two take to complete the race?

MAILBOX: LAST WEEK’S SOLVERS

#Puzzle 63.1

Dear Kabir,

#Puzzle 63.1
#Puzzle 63.1

The spider would travel a total of 420 inches: 140 inches on the 500-inch pole, then 240 inches on the 375-inch pole.

Since one end of the 375-inch pole rests 225 inches above the ground, the width of the road is

√ (375² – 225²) = 300 inches.

The height of the top end of the 500-inch pole is

√ (500² – 300²) = 400 inches.

The intersection divides the two poles in the ratio 400:225, or 16:9. So, the spider traverses the 500-inch pole for 500*9/25 = 180 inches, and the 375-inch pole for 375*16/25 = 240 inches.

Total distance traversed = 180 + 240 = 420 inches.

— Group Captain RK Shrivastava (retired), Delhi

#Puzzle 63.2

Hi,

The movies are as follows:

RUT AT KIWILAND: wait Until dark

(it appears that there is a slight mistake in this anagram, which should be RUT AT KIWILAND)

FAMILY YARD: mY FaiR LaDy

HUSTON’S ENTRY: tHE nUn’s story

ADAM, BORN IN IRAN: roBin and MariaN

CAN WE PARADE: wAr and PeacE

The anagram we get is URYRDHEUBNAPE, which gives AUDREY HEPBURN, the famous Hollywood actress of yesteryear.

— Ajay Ashok, Mumbai

Indeed, as several readers have pointed out, the anagram misprinted as RUT AT KIWIKAND should have read RUT AT KIWILAND. Thankfully, all of them recognised the typo and proceeded to solve the puzzle.

Solved both puzzles: Group Captain RK Shrivastava (retired; Delhi), Ajay Ashok (Mumbai), Amit Khanna (Fremont, California), Prof Anshul Kumar (Delhi), Bhuvi Jain (Delhi), Dr Sunita Gupta (Delhi), Bhasker Mundhra (Ghaziabad), Rohit Khanna (Noida), Sakshi Tayal (Ghaziabad), C Subba Rao (Hyderabad), Akshay Bakhai (Noida), Shishir Gupta (Indore), Mohammed Zidane (Delhi), Amardeep Singh (Meerut), AR Kamal Passi (CPWD)

Solved #Puzzle 63.1: Dr Nakul Makkar (Noida), Kanwarjit Singh (Chief Commissioner of Income Tax, retired; Delhi), Yadvendra Somra (Sonipat), Anil Khanna (Ghaziabad), Sandeep Asthana (Ghaziabad), Naresh Dhillon (Gurgaon), Prisha Gupta (Amity International, Saket), Gurdeep Singh (Delhi), Vikas Nanda (Pathankot), NK Shrivastav (Chandigarh), Shri Ram Aggarwal (Delhi), Amar Lal Miglani (Mohali), Sushma Pandhi (Chandigarh), Arun Gupta (Greater Noida), Vivek Aggarwal (Bangalore), Vineet K Dargan (Delhi), YK Munjal (Delhi), Moolchandra Gupta (Pune), Darshil Srivastava, Shruti Garg, HP Choudhury, Tanika Gupta, Anjali Kashikar

Solved #Puzzle 63.2: Rakesh Sahni (Noida), Shawn Jacob (Navi Mumbai), Jasleen Kaur (Delhi), Sundarraj C (Bangalore), Dr GL Arora (Delhi), Hanit Kaur (Chandigarh), Chandramohan Vavullipathy (Mumbai)

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

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  • ABOUT THE AUTHOR
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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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