It is always interesting to see veteran puzzlers referring to one another in their writings. Among the writings of David Wells I came across a puzzle whose solution is credited to George Summers. Although Wells does not specifically state that the puzzle too came from Summers, that is probably the case.
Previous episodes of Problematics, of course, have referenced both Wells and Summer. As on previous occasions when I have run a puzzle that I have not created myself, I have modified it in order to insulate the answer from a Google search. The fundamentals in my following adaptation, however, remain the same as in the original version.
#Puzzle 188.1
An exhibit has been stolen from an art museum. There are three suspects: a painter, a sculptor, and an art collector. Certain clues have been interpreted by a descendant of Sherlock Holmes, who has proven conclusively that two of these persons were involved, one as the thief, and the other as an accomplice. The third suspect is entirely innocent, but knows which one is the thief and which one is the accomplice. We are not told how young Ms Holmes deduced all that, but we can rest assured that her powers of deduction are as sound as those of her illustrious ancestor.
Based on her deductions, the police conduct a long interrogation. Among the statements given by the suspects, the following are relevant:
“The painter is not the accomplice.”
“The sculptor is not the thief.”
“The art collector is not innocent.”
It is best that we spell something out clearly (although it should be self-evident): In each of the above statements, the speaker was referring to a suspect other than himself or herself. We are not told who made which statement, nor are we told whether one, two or all three suspects are among the speakers above.
We do know, however, that only the innocent person consistently spoke the truth while the other two suspects lied all through the interrogation. After much pressing, the police interrogator also revealed to me that at least one of the three statements above was made by the innocent person.
Which one is the thief?
#Puzzle 188.2
Imagine a state of the Indian Union with a mixed population in terms of income. Out of all its residents, exactly 5 million individuals earn a monthly salary that is less than ₹1 lakh. Every individual earns a real salary (zero excluded) in a whole number of rupees, i.e., there are no paise after a decimal point to complicate your calculations.
Among these 5 million, what is the minimum number of individuals who earn the same salary every month?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 187.1
Hi Kabir,
There are two possible solutions for Puzzle #187.1, as shown visually.
— Professor Anshul Kumar, New Delhi
#Puzzle 187.2
Hello Kabir,
The number 1,111,111 = 239 x 4649. One factor is the number of cats and the other is the number of mice. Logically, 239 cats killed 4649 mice each.
— Dr Sunita Gupta, New Delhi
Yes, the first puzzle has two possible answers. That was an oversight on my my part: If I had given one extra clue, the solution would have been unique. As things stand, either solution is correct. Apart from Anshul Kumar and Kanwarjit Singh, most readers have sent only one solution each.
Solved both puzzles: Professor Anshul Kumar (New Delhi). Dr Sunita Gupta (New Delhi), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Anil Khanna (Ghaziabad), Vinod Mahajan (Delhi), Ajay Ashok (Delhi), Shishir Gupta (Delhi), Sabornee Jana (Mumbai), Amarpreet (Delhi)
Solved Puzzle #187.1: Yadvendra Somra (Sonipat)
