In each scenario, the following are true:

• At least one alien is telling the truth, and at least one alien is lying
• Exactly one alien stole the cake

In each scenario, who stole the cake? Make sure to include an explanation of your answer.

1) 

Arglbzz: "I stole the cake"

Brthflum: "Arglbzz stole the cake"

Clonk: "Brthflum didn't steal the cake"

2)

Arglbzz: "Brthflum stole the cake"

Brthflum: "It's my birthday today"

Clonk: "Anyone with an odd number of letters in their name is lying"

3)

Arglbzz: "The alien who stole the cake is lying"

Brthflum: "Exactly one of us is lying"

Clonk: "Exactly two of us are lying"

4)

Arglbzz: "Clonk didn't steal the cake"

Brthflum: "Arglbzz stole the cake"

Clonk: "This problem has a unique solution"