Problem 23 · 2011 Math Kangaroo
Stretch
Logic & Word Problems
casework
Each one of the three birds Isaak, Max and Oskar has its own nest. Isaak says: “I am more than twice as far away from Max as I am from Oskar.” Max says: “I am more than twice as far away from Oskar as I am from Isaak.” Oskar says: “I am more than twice as far away from Max as I am from Isaak.” At least two of them speak the truth. Who is lying?
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Answer: B — Max
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Hint 1 of 2
The statements form a cycle, so they cannot all be true at once.
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Hint 2 of 2
Try making each bird the single liar and see which case lets the other two be truthful.
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Approach: test which single liar makes at least two statements consistent
- The three 'more than twice as far' claims cannot all hold together for any placement of nests.
- Assume each bird in turn is the liar and check whether the other two statements can both be true.
- Only if Max is lying can Isaak's and Oskar's statements both hold, so Max is lying.
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