Good girls and bad boys (7)
On an island, there is this strange pattern - boys always lie while girls always tell the truth. This time round, you encounter four children.
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The oldest one says, "Exactly one of us is a boy."
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The second one says, "Exactly two of us are boys."
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The third one says, "Exactly three of us are boys."
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The youngest one says, "All four of us are boys."
Let 1 denote boys and 0 girls. In order of birth, identify the gender of each child and convert it into a number accordingly. Submit your answer as a string of 4 ones and/or zeroes. For example, if all four are boys, then your answer is 1111.
The answer is 1101.
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1 solution
At most one of the four children are telling the truth, otherwise the number of boys would be inconsistent. It is also possible that all are lying. This would mean that the number of boys must be zero, meaning all are girls. But this would in turn mean all are telling the truth, resulting in a blatant contradiction. So exactly one of the four must be telling the truth. In other words, exactly one is a girl while the other three are all boys. This means only the third child is making a true statement so the third child is the only girl.
Our desired answer is 1101 (boy, boy, girl, boy).