Problem 6

Five students,

A,B,C,D,E

, took part in a contest. One prediction was the order

ABCDE

. No contestant finished in the predicted position, and no two contestants predicted consecutively actually did so. A second prediction was

DAECB

. Exactly two contestants finished in their predicted positions, and two disjoint pairs predicted consecutively actually did so. Determine the actual order.

Step 2 of 4: Use the first prediction

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CAEBD,\ DCAEB,\ DCEBA,\ EDACB

Detailed analysis

Impose that no student is in the position predicted by $ABCDE$ and that no predicted consecutive pair from $ABCDE$ is consecutive in the actual order. Combining these restrictions with exactly two correct positions in $DAECB$ leaves precisely the four displayed orders, as in the source enumeration.