5.1. The girl always tells the truth on Thursdays and Fridays, and always lies on Mondays. On the other days of the week, she may tell the truth or lie. One day, she was asked for seven days in a row, in which year she was born. For the first six days, the answers received were 2010, 2011, 2012, 2013, 2002, 2011. What answer could have been received on the seventh day? List all possible options.
Answer: 2011 or 2010

Solution. Note that if among the specified 6 days there were a Thursday and a Friday, then some two adjacent answers would be the same. Therefore, either the first day is Friday, or the last day is Thursday. From this, we get the answer options.