Problematics | Round table
Four men and four women sit in a circular arrangement. Who sits directly between two men?
There are some puzzles in which we have a set of variables with some specifics given, and some withheld. In some, for example an Einstein puzzle, we can determine the entire set of combinations. Then there are others in which we are asked to work out only one or more parts of the withheld information, but not all of it. In some cases, only that part can be determined; in others, the entire information can be established although the puzzle asks for only part of it.
The following puzzle (with the source of the original version credited within my adaptation) asks you for only one piece of information. If you can unearth any more details than what is being asked, the solver may choose to discuss it or ignore it. But do be sure to specify what is definitely being asked.
#Puzzle 159.1
Meet four couples at a dinner party: Mr and Mrs Ahmed, Mr and Mrs Bhardwaj, Mr and Mrs Chaturvedi, and Mr and Mrs Dasgupta. The venue is the home of one of the couples, but we are not told which couple is hosting and which three couples are the guests.
The eight individuals take their seats around a circular table at regular separations of 45°. George J Summers, who invented the original version of this puzzle, gives us the following hints:
1. Next to Mrs Ahmed sits Mr Bhardwaj, to her left.
2. Mr Bhardwaj and Mrs Chaturvedi sit directly opposite each other, separated by 180°.
3. Mrs Chaturvedi compliments the hostess for the quality of the food.
4. The hostess is the only person sitting directly between a married couple. “Directly between” means both partners in the couple are next to her, one on either side.
5. Only one person sits next to two men, one on either side.
Who is the one next to two men?
#Puzzle 159.2
Take a deck of 52 cards, ask a friend to shuffle them thoroughly, and then deal them face down into two equal piles. You ask if there are more red cards in the left-hand pile than black cards in the right-hand pile, or vice versa.
Your friend cannot answer. Can you?
MAILBOX: LAST WEEK’S ANSWERS
#Puzzle 158.1
Dear Kabir,
Your wife shook hands with 4 people.
Since all the 9 persons you asked gave different answers, and no one shook hands with themselves or their spouse, the only possibility is that one person (and only one) must have shaken no hands; and one (and only one) must have shaken all available hands, that is 8 – leaving out the spouse. All numbers 0 to 8 take up the 9 slots. Your count must have been a repeat of one of these numbers, but you were out of the analysis.
One person shook hands with 8 people, or every person in the room other than his or her spouse. So, the “0 handshakes” slot can go only to this person’s spouse, who obviously was not included in those 8 handshakes.
With 8 and 0 accounted for, the next highest number of handshakes is 7. This person’s spouse must have shaken hands with only 1 person. Following this logic, the next couple would have shaken 6 and 2 hands respectively, and the following one 5 and 3. That leaves one couple who would have shaken 4 hands each – and that can only be your wife and you, since we have already established that you craftily left yourself out of the study to establish the rule of no repeats.
— Sanjay Gupta, New Delhi
#Puzzle 158.2
Dear Mr Kabir,
I have been solving Problematics puzzles for a long, but this time it took me many hours to finalize the solutions amidst a busy schedule. Nevertheless I could solve both puzzles to my satisfaction.
In the second puzzle, let M, D and P be the times taken by Mickey, Donald and Popeye respectively to complete the job when each is working alone. Their hourly rates are thus 1/M, 1/D and 1/P. From the given conditions we can set up three equations:
1/M + 1/D = 1/8
1/M + 1/P = 1/9
1/D + 1/P = 1/10
Solving, we get M = 14.69 hours, (Mickey’s time), D = 17.56 hours (Donald’s time), and P = 23.22 hours (Popeye’s time).
— Shri Ram Aggarwal, New Delhi
Solved both puzzles: Sanjay Gupta (Delhi), Shri Ram Aggarwal (Delhi), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Vinod Mahajan (Delhi), Dr Sunita Gupta (Delhi), Yadvendra Somra (Sonipat), Professor Anshul Kumar (Delhi), Ajay Ashok (Delhi), Sampath Kumar V (Coimbatore)
Solved # Puzzle 158.2: Dr Vivek Jain (Baroda), YK Munjal (Delhi), Shishir Gupta (Indore)
Problematics will be back next week. Please send in your replies by Friday noon to problematics@hindustantimes.com.
