Brain Teasers
Truth Day
On one of the seven days of the week, Hans Ernest Froopaloop, Jr. always tells the truth. On each of the other six days, he always lies.
One day he said, "I always lie on Sundays and on Mondays." The next day he said, "Today is either Wednesday, Friday, or Saturday." The next day he said, "I always lie on days beginning with T."
On which day does Mr. Froopaloop tell the truth?
One day he said, "I always lie on Sundays and on Mondays." The next day he said, "Today is either Wednesday, Friday, or Saturday." The next day he said, "I always lie on days beginning with T."
On which day does Mr. Froopaloop tell the truth?
Hint
Today and tomorrow do not count as "days beginning with T".Answer
Mr. Froopaloop always tell the truth on Monday.Mr. Froopaloop's first and third statements obviously cannot both be true. If they are both lies, then he tells the truth on one of Sunday and Monday, and he also tells the truth on one of Tuesday and Thursday, so this cannot work either. Therefore, one of Mr. Froopaloop's first and third statements is true and the other is false. His second statement must also be false.
Suppose Mr. Froopaloop's first statement is true. Since his third statement is false, he must have told the truth on Tuesday or Thursday, so his second statement must have been made on Wednesday or Friday. But since his second statement is false, this cannot work.
This means Mr. Froopaloop's third statement is true. Since his first statement is false, he must have told the truth on Sunday or Monday, so his second statement must have been made on Saturday or Sunday. But since his second statement is false, he could not have made that statement on Saturday, and it must have been on Sunday, which means he would have told the truth on Monday.
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