Problem 28 · 2022 Math Kangaroo
Stretch
Logic & Word Problems
casework
Mowgli asks a bear and a panther what day of the week it is. The bear always lies on Monday, Tuesday and Wednesday; the panther always lies on Thursday, Friday and Saturday. On every other day both tell the truth. The bear says, “Yesterday was one of my lying days.” The panther says, “Yesterday was also one of my lying days.” On which day did this conversation take place?
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Answer: A — Thursday
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Hint 1 of 2
Each animal claims 'yesterday was one of MY lying days'; an animal telling the truth today is honest, while a liar inverts its claim.
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Hint 2 of 2
Check each weekday: decide for the bear and panther whether today is truth or lie, then test if both statements can hold.
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Approach: test each weekday against both animals
- The bear lies Mon-Tue-Wed; the panther lies Thu-Fri-Sat; both tell the truth on Sunday.
- On Thursday the bear tells the truth and yesterday (Wed) really was its lying day; the panther lies today, and since yesterday (Wed) was not its lying day, its statement is false as required of a liar.
- Both statements are consistent only on Thursday, so the answer is A.
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