Task 2 - 040912 At the school sports day, Christian (C), Bernd (B), Alfred (A), and Dieter (D) had qualified for the final 100 m race. Based on their preliminary run times, it was expected that they would finish in the order $C B A D$. However, neither the position of any runner nor any pair of directly consecutive runners was correctly predicted. The physical education teacher expected the order to be $A D B C$. This was a good guess; because two runners did come in at the expected positions.

In what order did the runners finish the race?
There are 6 cases to investigate when considering the expectation of the sports teacher, as 2 positions are correct. The remaining two positions arise by swapping the expectations of the sports teacher for these two positions.

Case distinction:

1. ADCB - ruled out, as the sequence $\mathrm{AD}$ cannot occur according to the general expectation.
2. ACBD - ruled out, as D would then be correct in the 1st estimate.
3. ABDC - ruled out, as B would then be correct in the 1st estimate.
4. CDBA - ruled out, as C would then be correct in the 1st estimate.
5. BDAC - ruled out, as A would then be correct in the 1st estimate.
6. DABC - the only solution.