Problematics | Who is the postman?
A logic puzzle in which three salaried men called Gagan, Kiran and Suman are married to artists called Gagan, Kiran and Suman.
One of the most enduring puzzles from the English pioneer Henry Ernest Dudeney (1857-1930) involves six persons sharing three names. That is to say, two persons each share the same name. Clues are given about their profession, address etc, and the solver tries to establish the identity of one or more of the individuals.
Later generations of puzzlers have used Dudeney’s template to create newer logic puzzles in the same mould. Here in Problematics, I have taken inspiration from several other Dudeney puzzles, but this is my first attempt at using his 6-persons-with-3-names template.
Puzzle #146.1
Some names are gender-neutral; they can be given to either boys or girls. Therefore, meet three men called Gagan, Kiran and Suman and three women called (you guessed it) Gagan, Kiran and Suman. They happen to be three married couples, but we are not given the full details of which one is whose spouse.
The men are salaried individuals: a paramedic at a hospital, a plumber engaged by a housing society, and a postman in government service. Among the women, one is a painter, one a poet, and one a playwright.
The three couples live on the same street. The female Gagan and her paramedic husband live at the north end of the street, and the female Kiran and her plumber husband at the south end. The plumber’s best friend, incidentally, is the male Suman. The female Suman, meanwhile, lives in the middle of the street with her postman husband.
Although a career in the arts does not bring a fixed income, one can earn a windfall from a single painting exhibition, a successful book of poems, or one hit play. The female Suman, for example, had a very good year, earning three times as much as her husband. The woman with the same name as the paramedic, meanwhile, earned ₹10 lakh for the year. To prevent any misdirection, the year’s total income for each of the six individuals was an exact multiple of ₹1 lakh.
What is the postman’s name?
Puzzle #146.2
SCAN OF CAIRNS (2 words)
SONIA AND LIPI (1 word)
A MAN’S ACTION (2 words)
SO, I’M IN NEPAL (1 word)
LONG LEASES (2 words)
LANE OWNERS (2 words)
Unscramble the above anagrams to get the names of six cities, all in the same country.
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 145.1
Dear Mr Kabir,
Let the number of duck eggs = N, which means the number of chicken eggs = (100 – N). On the first day, both sets fetch the same price, i.e.
(N) (price of a duck egg) = (100 – N) (price of a chicken egg)
On the second day, after the baskets are interchanged unintentionally, the given facts can be represented as follows:
Price of a duck egg on the second day = 280/N = price of a chicken egg on the first day;
Price of a chicken egg on the second day = 630/(100 –N) = price of a duck egg on the first day
Substituting these values in the first day’s equation, we get
(N)[630)/(100 – N)] = (100 – N)[280/N]
=> 630N² = 280(100 – N)²
=> 70 x 9N² = 70 x 4(100 – N)²
=> [3N]² = [2(100 – N])²
Taking the positive square roots of both sides,
3N = 2(100 – N) => N = 40.
Thus the number of duck eggs is 40, and the number of chicken eggs is 100 – 40 = 60. This gives the first-day price of a duck egg (= second-day price of a chicken egg) as 630/60 = ₹10.50, and the first-day price of a chicken egg (= second-day price of a duck egg) as 280/40 = ₹7.
Sale on day #1 = (40 x 10.50) + (60 x 7) = ₹840; and sale on day #2 = 280 + 630 = ₹910. Thus Father should be happier on Day #2.
— Shri Ram Aggarwal, New Delhi
#Puzzle 145.2
Hello,
In the puzzle with playing cards, start by placing the 4s. There are only two options:
4 __ __ __ __ 4 __ __
__ 4 __ __ __ __ 4 __
By a process using trial and error, the second option is eliminated. The final solution is
4 A 3 A 2 4 3 2
— Biren Parmar, Bay Area, California
***
Position: 1 2 3 4 5 6 7 8
Cards: 4 A 3 A 2 4 3 2
Mirror solution
Cards: 2 3 4 2 A 3 A 4
— Vinod Mahajan, New Delhi
Solved both puzzles: Shri Ram Aggarwal (Delhi), Biren Parmar (Bay Area, California), Vinod Mahajan (Delhi), Abhinav Mital (Singapore), Anil Khanna (Ghaziabad), Dr Sunita Gupta (Delhi), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Shishir Gupta (Indore). Yadvendra Somra (Sonipat), Professor Anshul Kumar (Delhi), Sabornee Jana (Mumbai), Ajay Ashok (Delhi), Sampath Kumar V (Coimbatore)
Solved #Puzzle 145.1: Nitin Trasi (Sydney)
A note on #143.1: Two weeks ago, the list of correct solvers for an Einstein puzzle (#143.1) had omitted the name of Vinod Mahajan. He has since explained the way he interpreted some of the clues, and I have subsequently accepted his answer as correct. In future, I will try and make sure that every clue in an Einstein puzzle is worded in a way that there is no possibility of ambiguity in interpreting it.
Problematics will be back next week. Please send in your replies by Friday noon to probelmatics@hindustantimes.com.
