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Difficulty: MediumAnalytical Puzzles and Grouping

Five state government departments—Agriculture, Defense, Education, Finance, and Health—are scheduled to present their annual budget proposals sequentially from 1st to 5th. Consider the following conditions:
1. The Agriculture Department presents immediately after the Finance Department.
2. The Health Department presents at some point before the Education Department, but does not present first.
3. The Defense Department presents fifth (last).
4. The Education Department presents at some point after the Agriculture Department.

Arrange the five departments in the correct sequential order of their presentation from 1st to 5th.

  1. 1Finance Department
  2. 2Agriculture Department
  3. 3Health Department
  4. 4Education Department
  5. 5Defense Department

Answer

The correct sequential order of presentation from 1st to 5th is: Finance Department, Agriculture Department, Health Department, Education Department, and Defense Department.
Defense is fixed in the 5th slot. The consecutive pair [Finance, Agriculture] must fill slots 1 and 2 because placing them in slots 2 and 3 would force Health into slot 1 (violating the constraint that Health cannot present first). With slots 1, 2, and 5 filled by Finance, Agriculture, and Defense respectively, Health and Education must fill slots 3 and 4 in that order to satisfy the requirement that Health presents before Education.

Step-by-Step Solution

1
Identify fixed position constraints
Defense Department is fixed in position 5.
Condition 3 explicitly states Defense presents fifth.
2
Analyze adjacent block requirements
Finance Department and Agriculture Department form an ordered adjacent pair [Finance, Agriculture].
Condition 1 states Agriculture presents immediately after Finance.
3
Determine valid placement for the block [Finance, Agriculture]
[Finance, Agriculture] must occupy positions 1 and 2.
If [Finance, Agriculture] occupied positions 2 and 3, Health would have to be in position 1 to precede Education, but Condition 2 prohibits Health from being first. If [Finance, Agriculture] occupied positions 3 and 4, Education could not be placed after Agriculture because position 5 is taken by Defense.
4
Assign remaining positions for Health and Education
Health Department takes position 3 and Education Department takes position 4.
Positions 1, 2, and 5 are occupied. Condition 2 requires Health to precede Education, so Health is 3rd and Education is 4th.

Key Concept

Analytical Puzzles and Grouping
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Topics

Analytical Puzzles and Grouping

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