Salesmen & engineers
It is known that salesmen always tell the truth and engineers always tell lies. B and E are salesmen. C states that D is an engineer. A declares that B affirms that C asserts that D says that E insists that F denies that G is a salesman. If A is an engineer, how many engineers are there?
The answer is 3.
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1 solution
Lol, I first misread this problem to say that salesmen always lie and engineers always tell the truth. Bias showing!
We are told that A is an engineer, while B and E are salesmen.
C states that D is an engineer. Either C is telling the truth, i.e., C is a salesman and D is an engineer, or C is lying, and thus C is an engineer and D is a salesman. In either case, exactly one of the two is a salesman while the other is an engineer. Thus exactly two of { A , B , C , D , E } are lying engineers.
With this is mind, the statement " A declares that B affirms that C asserts that D says that E insists that" can be re-written as "it is true that". The two engineers of the five will reverse the negations of each other.
We are left with " F denies that G is a salesman" which is equivalent to " F asserts that G is an engineer". As with C and D , this statement implies that exactly one of these two is an engineer while the other is a salesman. Thus there are three engineers in all.