logic puzzle
- setting a question (for an exam)
- There are two types of islands: Tribe A, which always says the right thing, and Tribe B, which always lies.
- There are three natives; when I asked the first one his race, he answered in the local language, so I didn’t know.
- I asked the second, “What did he say?” I replied, “He said he was Tribe B.” The third person countered, “No, no, he said he was Tribe A.”
- Who is lying, the second or the third?
- answer
- The excellent part of this puzzle is asking who is lying, the second or the third person.
- It is not possible to determine if the first person is lying.
- If the first person is Tribe A, they honestly say they are Tribe A. If they are Tribe B, they lie and say they are Tribe A.
- So there is no way to answer, “It’s Tribe B.”
- From this we know that the second person is lying.
Is an irrational power of an irrational number ever a rational number?
- Consider the numbers [$ x = \sqrt{2}^{\sqrt{2}}, y=x^{\sqrt{2}}=(\sqrt{2}^{\sqrt{2}})^{\sqrt{2}} = \sqrt{2}^2 = 2
- Drawing useful conclusions without specifying whether x is a rational or irrational number
- If x is a rational number, this is an example of “an irrational number whose irrational power is rational”
- If x is an irrational number, then y is an example of “an irrational number whose irrational power is a rational number”
- Therefore, we can say “there are rational numbers for which the irrational power of an irrational number is a rational number”.
Blind spot card 1027 #blind spot card with no picture yet
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