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 1 of 4: Record the predictions

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ABCDE and DAECB

Detailed analysis

The first prediction is $ABCDE$ , and the second is $DAECB$ . We must enforce all conditions simultaneously.