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.
Four chamsonels A, B, C and D are conversing among themselves. A visitor from a neighboring planet, who is color blind, asks each of the four chamsonels their color and typer. They say:
A's response
1. B and myself are the same color and type.
2. I am blue.
3. C is a philosopher.
B's response
1. A's statements are false.
2. C and myself are the same color.
3. D and myself are the same type.
C's response
A and D are different colors, but the same type.
D's response
A and B are the same color, but different types.
What color and type are each of the four chamsonels?
Assume A is telling the truth. Then (according to A1), B is telling the truth also. But B1 asserts that A is lying, so our assumption is false and A is lying and therefore B1 is true.
From A2 (false) we know that A is pink and is therefore a logician.
From A3 (false) we know that C is a logician.
Assume D is telling the truth.
Then B is pink (the same color as A) but a philosopher
And from B3, D is also a philosopher and therefore also also pink.
And from B2, C is also pink, so everybody is pink!
This seems consistent, and is one solution:
A -- pink logician (liar)
B -- pink philosopher (truth)
C -- pink logician (liar)
D -- pink philosopher (truth)
Are there any other solutions? Well, assume that D is lying.
Then B must be a blue logician.
From B3, D must be a logician, and therefore pink.
But this means that C is lying, so C must be a pink logician.
And this contradicts B1, so the solution given above is the only one.
Analytical solution (spoiler)
