Problematics | Games people play with sets of matches
This week, I bring you two puzzles: One involves a game from the past and the other, a sneak peek into a part of my day. Good luck!
Back in the day when the Internet was accessible only to time travellers into the present, we amused ourselves mostly with pen and paper, dice and counters, or matchsticks. Some of these amusements have survived: people still solve cryptic crosswords and play tic-tac-toe and Scrabble, but matchstick games and puzzles have gone out of fashion as far as I can tell.
So, let’s go back to matches.
It’s a game between two players and involves 33 matches, which are laid out on a table in whatever arrangement. Meet an ace player teaching the rules to a gullible amateur.
Ace Player: Remove 1, 2, 3 or 4 matches from the table. Remember, at least 1, but not more than 4.
Gullible Amateur: Removed matches as advised.
AP: Now my turn to remove 1, 2, 3 or 4 matches. Here, I have done that. Your turn again, now.
GA: How long will this go on?
AP: Until all the matches have been removed. The player who removes the last match or matches is the loser.
The amateur soon finds that the ace wins every time. What is the strategy?
| #Puzzle 33.2: |
Every evening after work, I take the same Metro train and reach the station nearest our home at exactly 8 pm, from where my wife drives me home. She has perfected her timing; she leaves home at the same time every evening and reaches the station at exactly 8 pm, just as I emerge from the gates. One day, I took an earlier train and came out of the station at 7 pm. Not wishing to disturb my wife, I started to walk home. Unaware that I was already on my way, she started out at her usual time and met me on the way. Without wasting an instant, she picked me up and drove home. We found that we reached home 20 minutes earlier than usual. For how many minutes did I walk? |
Mailbox: Last week’s solvers:
| #Puzzle 32.1: |
Let us say he selects 'A' cards. So, the card he memorised is at the Ath position from the top. Let the name of the celebrity have (A + B) letters. We deal (A + B) cards, one card per letter. As the memorised card was at the Ath position, we have to deal another B cards after this. After we deal these one by one and place them back on the deck, their order gets reversed. Hence the memorised card now has B cards above it. When we place back the initially removed A cards, we have (A + B) cards above the memorised card. These cards get removed when the celebrity’s name is spelt out the second time, and the memorised card comes on the top of the rest of the deck. When we turn over the next card, it is the card memorised. And that is the magic. — Sunita and Naresh Dhillon, Gurgaon [The above puzzle drew a mix of right and wrong answers. To discuss where some of them got it wrong, let’s denote the number of cards selected as x, and the number of letters in the celebrity’s name as y. A few readers have wrongly argued that when the cards are reversed, the chosen card goes to the position (y – x). The position is actually (y – x + 1), as many other solvers have pointed out.] |
#Puzzle 32.2: Hello Kabir, On the left side we have assumed the number of terms to be odd and on the right side we have assumed it to be even. If we take an odd number of terms, we get 1 as the sum while taking an even number of terms we'll get 0 as the sum. — Parth Agrawal, DPS RK Puram |
| Solved both puzzles: Sunita & Naresh Dhillon (Gurgaon), Parth Agrawal (DPS RK Puram), Dhruv Phalod (Mumbai), Dr Nakul Makkar (Noida), Jasvinder Singh (Nabha), Sabornee Jana (Mumbai), Sarang Sule (Mumbai), Madhuri Patwardhan (Thane), Amardeep Singh (Meerut), Rahul Agarwal (Bay Area, California), Lucky Singh Randhawa (Mandawali, Delhi), Akshay Bakhai |
| Solved #Puzzle 32.1: Anushka Bandopadhyay (Fardidabad), Nathan Sequeira (Mumbai) |
| Solved #Puzzle 32.2: Dr Sunita Gupta (Delhi), Tanishq Gard (Sirsa), Aarika Goel (Gurgaon), Deviprakash Seksaria (Navi Mumbai), Amar Lal Miglani (Mohali), Pranjal Pawan Malpani, Y K Munjal, Sumit Sharma, Sandeep Bhateja (Hoshiarpur) |
Problematics will be back next week. Please send in your replies by Friday noon to problematics@hindustantimes.com
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