A small group of people makes a number of statements, some of which are true and some false. You are not told which statements are true, but there is usually a hint: a certain number of statements is true and the rest are false. You have solved a number of such puzzles over the years.
In the following variation, you don’t know who said what, or how many statements are true or false. All you know is about the truthful or lying nature of the speakers, whoever they are. You will find it quite a challenge, but it is solvable.
#Puzzle 217.1
Three sisters, who act on stage, television and in cinema respectively, look so much like one another that no one knows who is older and who is younger. When a fan asks them, he gets the following replies:
1. The stage actress is not the eldest.
2. The TV actress is not the second eldest.
3. The film actress is not the youngest.
The fan remains clueless as ever until the actresses’ mother gives him a few clues.
“Not all the statements you heard were true, you know,” she says.
{{/usCountry}}“Not all the statements you heard were true, you know,” she says.
{{/usCountry}}“Which ones were true?” the fan wants to know, although he does not remember who made which statement.
“Only my youngest daughter told the truth. Every statement she made was true. Every statement made by either of my other two daughters was false.”
“Well,” the fan asks, “how many statements did the youngest make?”
“I shall not disclose the exact number,” says the mother, “but my youngest did make at least one of the three statements.”
“Any other clues?”
“None of my daughters spoke about herself,” the mother replies. “Each statement was about one or the other of the speaker’s sisters.”
“In that case,” says the fan, “I think I have worked out who is who.”
Can you?
#Puzzle 217.2
Three male members of a family are resentful about having to share an inheritance with a woman relative.
Man #1: If I had the woman’s inheritance in addition to my own, I would be twice as rich as the other two men.
Man #2: If I had her inheritance in addition to my own, I would be three times as rich as the other two men.
Man #3: If her inheritance were added to mine, I would be five times as rich as the other two men.
In what proportion is the inheritance being split among the four?
(Adapted from a problem by Mahavira in Gamta-Sara-Sangraha)
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 216.1
Dear Kabir,
The original number before multiplication is 142857.
Depending upon the multiplier(red card), the performer changes the start point of the sequence by cutting the pack as below:
2: 285714
3: 428571
4: 571428
5: 714285
6: 857142
— Yadvendra Somra, Sonipat
#Puzzle 216.2
Hello Kabir,
All the anagrams are the names of Nobel laureates
TORCH BROKE = ROBERT KOCH (Medicine, 1905)
ESTATE IN BERLIN = ALBERT EINSTEIN (Physics, 1921)
RENDERERS OF TRUTH = ERNEST RUTHERFORD (Chemistry, 1908)
PURE BLACK = PEARL BUCK (Literature, 1938)
THERE’S A METRO = MOTHER TERESA (Peace, 1979)
MORONS LOITER = ELINOR OSTROM (Economics, 2009)
— Dr Sunita Gupta, New Delhi
One reader asks whether the anagram of PEARL BUCK should have been of PEARL S BUCK instead. Historically, she has been referred to both ways. While her full name including the middle initial commonly appears on her books and film adaptations, she is also widely recorded and credited simply as Pearl Buck. Either form is widely recognised and acceptable.
Solved both puzzles: Dr Sunita Gupta (Delhi), Kanwarjit Singh (Chief Commissioner of Income-tax, retired). Professor Anshul Kumar (Delhi), Sabornee Jana (Mumbai)
Solved #Puzzle 216.1: Yadvendra Somra (Sonipat), Anil Khanna (Fremont), YK Munjal (Delhi), Shishir Gupta (Indore)