Aidan, Benedict, Clint, and Dwayne are all brothers, with precisely two of them being twins.
• At least one of them is a Truthteller and makes all true statements.
• At least one of them is a Liar and makes all false statements.
• At least one of them is an Alternator and makes alternating true and false statements, or vice-versa.
• The two which belong to the same type are the twins.

Three of the four brothers make the following statements:

Aidan:
---------
1) Benedict is one of the twins.
2) Clint is a liar.

Benedict:
--------------
1) Clint is one of the twins.
2) Aidan is a truthteller.

Clint:
-------
1) I am not one of the twins.

Determine who are the twins from the statements given above.   What are the respective types of the four brothers?


Solution to the Problem:


Assume Clint is one of the twins.   Then Clint's statement 1 is false, and Benedict's statement 1 is true.

If Benedict were a Truthteller, then Aidan would also be a Truthteller, which can't happen.   If Benedict were an Alternator then Clint must be an Alternator as well.
So Aidan makes one true statement, and one false statement, but there's fewer than 3 Alternators.   So this can't happen.

Thus, Clint is not one of the twins.   So Clint's first statement is true, and Benedict's first statement is false.

Since Clint makes a true statement, he can't be a Liar, so we see that Aidan makes at least one false statement, and thus both Benedict's statements are false.
If Benedict is not one of the twins, then Aidan is a Liar and Benedict is a Liar, which can't happen.

So Benedict is one of the twins, then Aidan is an Alternator, Benedict is a Liar, and Clint is a Truthteller, which means Benedict and Dwayne are twins.

Consequently, summarizing the foregoing, we have:

Benedict and Dwayne are the twins.
Benedict and Dwayne are the Liars.
Clint is the Truthteller.
Aidan is the Alternator.

Correctly solved by:

1. Colin (Yowie) Bowey Beechworth, Victoria, Australia
2. Ritwik Chaudhuri Santiniketan, West Bengal, India
3. Seth Cohen Concord, New Hampshire
4. Dr. Hari Kishan D.N. College,
Meerut, Uttar Pradesh, India
5. Ivy Joseph Pune, Maharashtra, India
6. Neha Benny Cochin, Kerala, India
7. Cory Creel ----------
8. Davit Banana Istanbul, Turkey
9. Kelly Stubblefield Mobile, Alabama