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Question

Difficulty: MediumOrder and Ranking

Five cargo ships—Apex, Beacon, Crest, Dawn, and Echo—arrived at a port one after another. Based on the following conditions, arrange the ships in the correct order of their arrival from first to last:

1. Crest arrived exactly two places after Beacon.
2. Dawn arrived before Echo but after Beacon.
3. Apex did not arrive first or last.
4. Echo arrived immediately after Apex.

Arrange the cargo ships in chronological order from the first to arrive to the last.

  1. 1Beacon
  2. 2Dawn
  3. 3Crest
  4. 4Apex
  5. 5Echo

Answer

The correct chronological order of arrival is Beacon, Dawn, Crest, Apex, and Echo.
The conditions are uniquely satisfied when Beacon is 1st, Dawn is 2nd, Crest is 3rd, Apex is 4th, and Echo is 5th. Beacon must be first because placing it anywhere else either pushes Crest too far back or prevents Dawn and Echo from following their respective constraints.

Step-by-Step Solution

1
Determine the relative positions of Beacon and Crest.
Beacon is in position xx, and Crest is in position x+2x+2.
The condition states that Crest arrived exactly two places after Beacon.
2
Determine the possible positions for Apex and Echo.
Apex and Echo must occupy consecutive positions, with Apex directly before Echo. Since Apex cannot be first or last, they can only occupy positions 2 and 3, 3 and 4, or 4 and 5.
Echo arrived immediately after Apex, and Apex has boundary restrictions.
3
Test position assignments to satisfy all constraints.
If Beacon is 1st, Crest is 3rd. This leaves positions 4 and 5 for Apex and Echo. Dawn must arrive after Beacon and before Echo, so Dawn perfectly fits into the remaining 2nd position.
If Beacon were placed 2nd or later, it would create unresolvable conflicts with the spacing needed for Apex and Echo, or violate Dawn's placement.

Key Concept

Relative ordering and positional constraints
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Topics

Order and Ranking

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