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A, B, C, and D are four positive integers whose sum is 2019. What are the largest and smallest values that A*B+B*C+C*D can be?
(No Solution Yet, 0 Comments) Submitted on 2019-06-15 by Brian Smith   
Difficulty: 3 of 5 Bonus: A Chamsonel Problem (in Liars and Knights) Rating: 3.00
The dominant species in Planet Blancneldos is the chamsonels. There are two types of chamsonels - logicians and philosophers. The chamsonels also have two different skin colors related to their veracity. Pink logician chamsonels always lie while blue logician chamsonels always tell the truth. Pink philosopher chamsonels always speak truthfully but blue philosopher chamsonels always speak falsely.

Three chamsonels A, B and C are approached by a visitor from a neighboring planet who asks each of their skin color and type. Their responses are given below. It is known that the visitor is color blind.

As response:

1. Precisely two of us speak the truth and I am one of them.
2. B is blue.
3. I am not pink.

Bs response:

1. C and myself always speak the truth.
2. I am a philosopher.

Cs response:

1. A and myself always speak the truth.
2. I am blue.
3. I am the only logician amongst the three of us.

What are the type and skin color of each chamsonel?

(Solution Posted, 7 Comments) Submitted on 2007-01-30 by K Sengupta   
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