Good girls and bad boys (3)

Logic Level 1

On an island, there is this strange pattern - boys always lie while girls always tell the truth. You encounter two children.

The older one says, "We are of the same gender."
The younger one says, "I have an elder sister."

Who is speaking to you?

Older sister, younger brother Two sisters Older brother, younger sister Two brothers

2 solutions

Noel Lo
Jan 27, 2016

If the older one is a girl, then we indeed have two of the same gender since girls tell the truth. This means she has a younger sister. As a girl, her younger sister will also be correct in saying that she has an elder sister which tallies with our assumption.

However, suppose the older one is a boy. Then we would have two of the opposite gender since he is a liar. This means he has a younger sister. But we have a problem here. As a girl, his younger sister must tell the truth. But we know the statement "I have an elder sister" is false since we assumed the older one to be a boy, not a girl.

So only the first case works and we have our answer.

Since we aren't told that the children are necessarily related, the older child could be a boy and the younger child a girl, who does have an older sister but this older sister does not happen to be present at this encounter.

Brian Charlesworth - 3 years, 3 months ago

Saya Suka
Mar 6, 2021

Whenever somebody claimed to be associated with another person / party in a bigger group, then we can be sure that the other person is a truth teller even when that someone who did the whole self-claiming business might do so deceptively, too. From this, we know that the younger sister is telling the truth with her "I have an elder sister" speech. They must be a pair of two sisters.

Good girls and bad boys (3)

2 solutions

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