\section*{Task 2 - 091232}

Four friends, Axel, Bodo, Christian, and Dieter, bought a boat. They agreed that each of them should conduct one of the first four trips. When determining the order of these trips, they expressed the following wishes:

1. If Dieter should go first, Christian wanted to go third.

2. If Axel or Dieter should go second, then Christian wanted to go first.

3. Then and only then, if Axel should go third, Bodo wanted to go second.

4. If Dieter should go third, then Axel wanted to go second.

5. If Dieter should go last, then Christian wanted to go third and Axel wanted to go first.

Determine all possible orders in which the first four trips can be conducted so that these wishes are fulfilled!
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We conduct a case distinction based on which of Dieter's trips is taken over:

Case 1: Dieter drives first. Then, according to 1., Christian drives third and, according to 3., Bodo does not drive second, so he must drive fourth, leaving only the second position for Axel. This results in the sequence Dieter, Axel, Christian, Bodo, which contradicts condition 2. Therefore, there is no valid solution in this case.

Case 2: Dieter drives second. Then, according to 2., Christian drives first and, according to 3., Axel does not drive third, so he must drive fourth, leaving only the third position for Bodo. This results in the sequence Christian, Dieter, Bodo, Axel. The verification confirms this solution.

Case 3: Dieter drives third. Then, according to 4., Axel drives second. According to 2., Christian drives first, and finally, Bodo drives fourth. This results in the sequence Christian, Axel, Dieter, Bodo. The verification confirms this solution.

Case 4: Dieter drives fourth. Then, according to 5., Christian drives third, Axel drives first, and Bodo drives second. This results in the sequence Axel, Bodo, Christian, Dieter, which contradicts condition 2, so there is no solution in this case.

Therefore, there are exactly two valid sequences.