Problem 30 · 2014 Math Kangaroo
Stretch
Logic & Word Problems
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2014 people stand next to each other in a row. Each person is either a liar (who always lies) or a knight (who always tells the truth). Each person says: “To the left of me there are more liars than there are knights to the right of me.” How many liars are in the row?
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Answer: C — 1007
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Hint 1 of 2
Translate each claim into 'liars on my left' vs 'knights on my right'.
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Hint 2 of 2
Track how those two counts change as you move along the row to find the only consistent split.
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Approach: reason about left-liars vs right-knights along the row (deferred to official key)
- A knight's claim 'more liars to my left than knights to my right' is true; a liar's is false.
- Working through how the two running counts must compare forces the count of liars.
- The number of liars is 1007.
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