E-Paper
Problematics | Family planning
Three friends discuss their sons and daughters. Who has how many children?
George J Summers is the author of several books on puzzles, including Mensa puzzles, but I could not find any biographical information on him from either a Google search or an AI query. The publication dates of his books cover a wide period from the 1960s to about a decade ago.
I have adapted the following puzzle from one of his books. I found it quite tough in its original form, and have added an embellishment in the hope that it will make the puzzle slightly simpler. You may need some hit and trial alongside logical deduction to solve it.
#Puzzle 154.1
Mrs Anand, Mrs Bora and Mrs Chopra are schoolmates who meet for the first time in about 20 years. They catch up on one another’s lives, careers and families. All of them are married with children, and each one has at least one daughter and more sons than daughters. In other words:
(1) Mrs Anand has twice as many sons as daughters.
(2) Mrs Bora has three more sons than daughters.
(3) Mrs Chopra has three times as many sons as daughters.
I ran into one of the three women the other day, and she gave me the above updates from their conversation.
“How many children do the three of you have in total?” I wondered.
She gave me a number less than 25.
“Thank you,” I said. “Now I know the exact number of sons and daughters you have. This means I also know the total number of children between your two friends, but I don’t know their individual totals.”
The woman helped me with more information: “My friend Mrs Bora has the fewest children among the three of us.”
“Ah,” I said, “now I know the number of children each of you has.”
Which of the three did I meet, and who has how many children?
#Puzzle 154.2
A woman and her two children are invited to lunch by the woman’s sister who lives in the next town. They start out from home at the same time. The daughter cycles at a brisk 15 kph and reaches her aunt’s home one hour before the appointed lunch hour. The son, who is new to cycling, travels at 10 km/h and arrives one hour late for lunch, much to his aunt’s annoyance. The mother, a veteran at solving Problematics puzzles, cycles at just the right speed that allows her to reach her sister’s home exactly at lunch hour.
What is the mother’s speed?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 153.1
Hi Kabir,
The four statements are re-written below with person names only (place names are removed).
(1) If Chitra is married then either Apsara or Bonnie is married but not both
(2) If neither Apsara nor Chitra is married then Bonnie must be married
(3) If Apsara is married then Bonnie and Chitra are both unmarried
(4) Bonnie is unmarried if both Apsara and Chitra are unmarried
From statements (2) and (4), we can infer that Apsara and Chitra (either of them or possibly both) are married. However, statement (3) rules out the possibility of both Apsara and Chitra being married. Therefore, either Apsara or Chitra is married, but not both. Now based on who among these two is married, we have either of the following two possibilities -
If Chitra is married and Apsara is unmarried, then Bonnie is married [according to (1)].
If Apsara is married and Chitra is unmarried, then Bonnie is unmarried [according to (3)].
In summary,
EITHER Apsara is married and both Bonnie and Chitra are unmarried,
OR Apsara is unmarried and both Bonnie and Chitra are married.
(PS: After looking at the 27 July 2025 edition of Problematics, I realised that although I had written up the solutions for Puzzle #152. 1 and #152.2, I had forgotten to mail them.)
— Professor Anshul Kumar, New Delhi
# Puzzle 153.2
Hi Kabir,
The number is 6210001000. It has six 0s, two 1s, one 2 and one 6.
— Shishir Gupta, Indore
Solved both puzzles: Professor Anshul Kumar (Delhi), Shishir Gupta (Indore), Dr Sunita Gupta (Delhi), Ajay Ashok (Delhi), Vinod Mahajan (Delhi), Shri Ram Aggarwal (Delhi)
Solved Puzzle #153.1: Yadvendra Somra (Sonipat), Rituparna Gupta (Indore)
Solved Puzzle #153.2: Dr Vivek Jain (Baroda)
Problematics will be back next week. Please send in your replies by Friday noon to problematics@hindustantimes.com
