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The Natives of Calendria (Posted on 2011-02-10) Difficulty: 2 of 5
In the kingdom of Calendria, the natives all lie during months with English names beginning with vowels and tell the truth in the other months. One native makes the following two statements:

  • I lied last month.
  • I will lie again six months from now.

In what month were the two statements made?

  Submitted by Charlie    
Rating: 4.5000 (2 votes)
Solution: (Hide)
If he were telling the truth, there'd be a month beginning with a vowel with another such month 7 months away, but there is no such separation. The closest that comes is the 6 months from April to October or vice versa.

So the knave is lying in both instances, so there's a 7-month interval from a truth-telling month to another such month, as the lying nature of his current statements make the months referred to as truth-telling months. Furthermore, the month at the beginning of that 7-month span must be followed by a lying month.

There are only 3 lying months, so let's see:

April is preceded by March, and 7 months after that is October, so that span is no good.

August is preceded by July, and 7 months after that is February. This works.

October is preceded by September, and 7 months after that is April. So, again, that doesn't work.

The only month that works is August and the knave is lying.

From The Mensa 365 Brain Puzzlers 2011 Calendar, from Page-a-Day publishing, by Mark Danna and Fraser Simpson. Puzzle for January 23.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolutionMath Man2011-02-12 13:08:42
SolutionSolutionhoodat2011-02-11 15:31:23
SolutionAnalysis & solutionJer2011-02-10 18:04:29
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