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 Smart Man (Posted on 2013-10-17)
Of Al, Ben and Cal, only one man is smart.
```Al says truthfully:
1. If I am not smart, I will not pass Physics.
2. If I am smart, I will pass Chemistry.

Ben says truthfully:
1. If I am not smart, I will not pass Chemistry.
2. If I am smart, I will pass Physics.

Cal says truthfully:
1. If I am not smart, I will not pass Physics.
2. If I am smart, I will pass Physics.```
It is known that:
```   I. The smart man is the only man to pass one
particular subject.
II. The smart man is also the only man to fail
the other particular subject.```
Which one of the three men is smart and why?

 See The Solution Submitted by K Sengupta Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Possible solution | Comment 1 of 3

I believe that direct contradictions can be found to supply a unique solution. Number the stipulations as follows:

A. Al says truthfully:
1. If I am (not smart), I will not pass Physics.
2. If I am smart, I will pass Chemistry.

B. Ben says truthfully:
1. If I am (not smart), I will not pass Chemistry.
2. If I am smart, I will pass Physics.

C. Cal says truthfully:
1. If I am (not smart), I will not pass Physics.
2. If I am smart, I will pass Physics.

D1. Either 2 pass Physics, and smart passes Chemistry, or
D2. 2 pass Chemistry, and smart passes Physics.

Case D1. We just need to consider Cal's case.
Assume Cal is (not smart): contradiction between C1 and D1
Now assume that Cal is smart: contradiction between C2 and D1.

Case D2. This time Cal is flexible.
Assume Cal is (not smart): no contradiction.
Now assume that Cal is smart: still no contradiction.
As to Al's case, assume that Al is smart: contradiction between A2 and D2
Now assume that Al is not smart: no contradiction.
As to Ben's case, assume that Ben is smart: no contradiction
Now assume that Ben is not smart: contradiction between B1 and D2.

So Ben must be smart, Al must be (not smart) , and by elimination, Cal is (not smart) also.

Edited on October 17, 2013, 11:30 am
 Posted by broll on 2013-10-17 11:26:59

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