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 3 of 4: Test the consecutive pairs

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AE

Detailed analysis

For $CAEBD$ and $DCAEB$ , the only correctly predicted consecutive pair from $DAECB$ is $AE$ . For $DCEBA$ , none of the predicted consecutive pairs is realized. Thus none has two disjoint pairs.