Problematics | Murder mystery
Police have three suspects and their statements, but not all of them are true. Who is the killer?
Problematics has occasionally had puzzles in which you cannot determine the complete set of variables, but can still settle specific questions with answers that remain the same in all possible circumstances. Some truth vs lie puzzles are like that.
The puzzle below, however, does not fall in that category as far as I can tell. It appears to have a unique set of answers: you can (a) establish the truth/falsehood of every statement given, (b) determine which person speaks the truth, lies or alternates between truth and falsehood, and (c) finally seal the question being asked at the end. If you find that multiple answers are possible, however, I shall be happy to be proved wrong, but please make sure that every statement is accounted for.
#Puzzle 164.1
A murder has been committed and a police officer rounds up three suspects from a gang where each member is infected with any of three diseases. Some of them always tell the truth, and some always lie. Those infected with the third disease, as you will have guessed, alternate between truth and falsehood. When anyone affected by the third disease gives you two statements, one must be true and the other false, but the order may be either true-false or false-true.
We know that each suspect is infected by one of the diseases. What we do not know is whether they are the same or different diseases. Maybe all three have the same disease. Maybe each one has a different disease. Or maybe a common disease has infected exactly two of them, while the third suspect has a different infection.
Each suspect gives two statements to the police officer:
Suspect #1: Exactly two of the three suspects have the same disease.
Suspect #2: The murderer is not Suspect #3.
Suspect #3: The murderer is not Suspect #2.
Suspect #1: I am not the murderer.
Suspect #2: The murderer always lies.
Suspect #3: Neither of the innocents has the same disease as the murderer.
Who has which disease, which statements are true and which are false — and, of course, who is the murderer?
#Puzzle 164.1
In a European football tournament, a win gives a team 2 points, a draw 1 point, and a loss no points — everything as usual. England, France, Germany, Hungary, and Italy are placed in the same group. Every team plays every other team in its group once. After these group matches are over, England have 6 points, France 5, Germany 3 and Hungary 1.
How many points for Italy?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 163.1
Hi Kabir,
The hidden number is 23900 and Jackie scores the highest with 4 correct digits. This is determined as follows: First, we check if any gambler had a score of 5. If a gambler had got all 5 digits correct, the number of matches between him and other gamblers would have been distinct for every gambler. But that is not the case as shown in the table.
Therefore, the five gamblers have got scores of 0, 1, 2, 3 and 4. This corresponds to 5, 4, 3, 2 and 1 as the number of mismatched digits. Using logic and further elimination, it can be seen that 23900 is the only number for which all five gamblers get distinct scores. Jackie (23990) has four digits correct. The other scores are Al Capone (11999) with 1 digit correct, Bonnie (22909) with 3 digits correct, Clyde (12990) with 2 digits correct, and Scarface (31099) with no digits correct.
— Professor Anshul Kumar, New Delhi
#Puzzle 163.2
In the multiplication TA x TA = ROT, the digits are T = 1, A=9, R= 3, O= 6, so that 19 x 19 = 361. This was not too difficult as the digit in the tens place of TA had to be 1, 2 or 3. I had to then think of digits whose square could have 1, 2 or 3 in the units place (if any), and it was obvious that it could only be 9.
— Kanwarjit Singh, Chief Commissioner of Income-tax, retired
Solved both puzzles: Professor Anshul Kumar (Delhi), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Dr Sunita Gupta (Delhi), Yadvendra Somra (Sonipat), Vinod Mahajan (Delhi), Sabornee Jana (Mumbai), Shishir Gupta (Indore)
Solved #Puzzle 163.2: Y K Munjal (Delhi), Shri Ram Aggarwal (Delhi), Ajay Ashok (Delhi)
