A stupid car thief stole the car allotted to the chief of police. The police started an investigation and arrested four suspects who were seen near the car at the time of the crime.
During the course of questioning, the suspects offered the following statements:
Arlo
- In senior high school, I was in the same class as Caleb.
- Bryce hasn't driven a car in his life.
- The thief didn't know that it was the car of the police chief.
Bryce
- Caleb is the guilty one.
- Arlo is not guilty.
- I haven't driven a car in my life.
Caleb
- In senior high school, I was in the same class as Arlo.
- Bryce is innocent.
- Arlo is the guilty one.
Diego
- Caleb is innocent.
- I didn't do it.
- Arlo is the guilty one.
It is known that:
- Precisely 4 of these 12 statements are true.
- At the time of committing the crime, the actual thief did not know that it was the Police Chief's car.
Determine the car thief from the above-mentioned clues.
I came to a similar conclusion as Charlie:
We assign the value of "1" to True and "0" to False, and leave open
the two questions: "was B never a driver?" P = (0 or 1) for Pedestrian, and "were A and C students together?" S = (0 or 1) for School. Then, hypothesizing sequentially A, B, C, or D, was guilty, we have the total truths count in each case. Total from the 12 questions, taken one possible thief at a time, as:
If A guilty: Total # of Truths = 2 S + 2 P + 6
If B guilty: Total # of Truths = 2 S + 2 P + 4
If C guilty: Total # of Truths = 2 S + 2 P + 5
If D guilty: Total # of Truths = 2 S + 2 P + 4
For the total to be 4, S must be false (value 0) and P must be false (value 0) and this would only work for B or D. So, as the problem stated, either B or D could driven the car away.
I suspect the driving statement was actually meant to be posed in the opposite sense, such as: "B was able to drive", and we'll use P for proficient. Then P would need to be false for Total=4, but this would simultaneously make it hard for B to steal the car (he can't drive), implying that D is the thief.
(The flaw in my puzzle revision here is this: "stupid thief" non-driver B could still have pushed the car off.)
Edited on May 18, 2022, 1:17 am
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