Problematics | When couples bought and sold puzzles
This week, a tweaked version of an unusual puzzle that was first published more than 200 years ago.
For more than a century, an English magazine called the Ladies’ Diary, initially consisting mainly of recipes, soon started to include mathematical puzzles of varying levels of difficulty. A bunch of these puzzles published between 1704 and 1816 is now available in a set of four volumes, which I hope to procure soon so that I can share the puzzles with Problematics readers.
As of now, I have access to a handful of those puzzles, published in other selections. The following one is based on a British currency system that is no longer in use. In that system, a guinea was 21 shillings, but I have simplified that by using ₹63 instead of three guineas. I have also done away with characters with European names, replacing them with (Indian) cities of origin. Tweaks aside, however, the essence of the puzzle is exactly as it was when it appeared more than 200 years ago.
Puzzle 115.1
There are three couples, the women coming from Agra, Beed and Churu, and the men from Dewas, Erode and Faridpur. We are not told who is married to whom. What we are told is (after my embellishments):
1. The six people buy puzzles at different prices.
2. Each person buys as many puzzles as the number of rupees they pay for one puzzle. In other words, if someone pays ₹2 per puzzle, they buy two puzzles. If someone else pays ₹10 per puzzle, they buy 10 puzzles. And so on.
3. Each husband spends ₹63 more than his wife spends.
4. Mr Erode buys 11 puzzles more than Ms Agra.
5. Ms Beed buys 23 puzzles fewer than Mr Faridpur.
Who is married to whom?
Puzzle 115.2
You have seven glasses that are overturned, as shown. You need to get all of them the right side up, but you cannot flip them one at a time. At any move, you can reverse any three glasses. Any glass reversed in one move can be reversed again in subsequent moves, if required.
In how many moves can you get all seven glasses the right side up (mouths upwards)?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 114.1
Hi Kabir,
The drone covered a distance of 8km between the two officers (both ways) before landing. This can be determined as follows. The speed at which the two officers covered the 10km between them is 1.5 + 1 = 2.5km/h, so the time they took is 10/2.5 = 4 hours. This means the drone also travelled for 4 hours . Since the drone’s speed is 2km/h, it travelled 2 x 4 = 8km, both ways.
— Shishir Gupta, Indore
#Puzzle 114.2
Dear Kabir,
Let the persons be designated as T (always speaks the truth), A (alternates between truth and falsehood) and F (always lies). The answers of T and F have to different for any card. In the first instance the answers of the first and second persons are the same, and in the second instance the answers of the second and third persons are the same. Therefore, the pair of first-and-second or the pair of second-and-third persons cannot be T-and-F or vice versa. Therefore, the T-and-F pair must be between the first and third persons, which means the second person is A. As the answers of A are the same on both instances, the cards have to be of different colours. From the information available, it is not possible to determine the sequence in which order the red and the black cards were shown.
— Yadvendra Somra, Sonipat
Solved both puzzles: Shishir Gupta (Indore), Yadvendra Somra (Sonipat), Vivek Jain (Baroda), Sanjay S (Coimbatore), Dr Sunita Gupta (Delhi), Anil Khanna (Ghaziabad), Kanwarjit Singh (Chief Commissioner of Income-Tax, retired), Sanjay Gupta (Delhi), Sabornee Jana (Mumbai), Professor Anshul Kumar (Delhi)
Solved #Puzzle 114.1: Ajay Ashok (Delhi), Shri Ram Aggarwal (Delhi)