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solution


Two-year Garden Solution Diagram Two-year Garden Vegetable Legend


detailed solution

From two summers ago (year one), the first two clues each produce L-shaped arrangements of sets of three crops.

  • The green peppers were just north of the yellow corn, and just west of the tomatoes.
  • The red peppers were just north of the lettuce, and just west of the green beans.
Detailed Solution Diagram A1

These two L-shaped arrangements can fit in a three-plot-by-three-plot square garden in only two possible ways.

Detailed Solution Diagram A2

  • The lettuce was right next to the broccoli.

The final clue for the first year does not eliminate either of these possibilities. Notice, however, that in one layout, there are two possible places that broccoli could go, whereas in the other layout, there is only one place that broccoli could go.

From last summer (year two), the first two clues also each produce L-shaped arrangements of sets of three crops. The final clue places two crops in a vertical alignment.

  • The yellow beans were just north of the red peppers, and just east of the tomatoes.
  • The green peppers were just south of the lettuce, and just west of the carrots.
  • The green beans were just north of the yellow corn.
Detailed Solution Diagram B1

These arrangements yield three possible layouts for the second year. One of these is impossible, because it does not allow for the third clue in the second year.

Detailed Solution Diagram B2

Pairing one of two possible crop arrangements from year one with one of two possible crop arrangements from year two produces four possible pairings. However, three of these pairings are elminated because of the requirement that no crop occupies the same plot of land over consecutive years.

Detailed Solution Diagram C

To summarize our progress, the position of six crops in each year have been determined, leaving three crops from each year to be placed.

Detailed Solution Diagram D1

  • The lettuce was right next to the broccoli.

The final clue for the first year can now be used, since there is only one possibility. Since the positions of the yellow beans and corn cannot be the same in the second year, their positions can also be determined.

Detailed Solution Diagram D2

  • The green beans were just north of the yellow corn.

The green beans and yellow corn pairing could be positioned in the remaining space in one of two ways, leaving brocolli at the top or bottom of the left-hand column. However, since brocolli was in the bottom left-hand corner in the first year, brocolii must be planted at the top in second year.

Detailed Solution Diagram D3