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 4 of 4: Identify the surviving order

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DA and CB

Detailed analysis

The order $EDACB$ contains the two disjoint predicted pairs $DA$ and $CB$ consecutively. It therefore satisfies the final condition, so the actual order is $\boxed{EDACB}$ .