Effie Gardner divided her vegetable garden into seven plots, labeling them A to G as shown, and planted a different vegetable in each plot (one was corn). From this information and the following clues, can you find which vegetable was planted in each plot?

1. 1  The beets and broccoli were planted in opposite corners of the garden; the broccoli plot borders more other plots than the beet plot does.
2. 2  The cabbage and peas plots each border the same number of plots, but the cabbage plot is bigger than the peas plot.
3. 3  The two root vegetables, beets and carrots, don’t border each other, and neither do the two legumes, peas and beans.
4. 4  The first letter of at least one vegetable is the same as the label of the plot it’s in.

Solving:

First take a deep breath and remind yourself this is only an exercise, that it has no easy, quick solution. Plan to spend some time figuring it out. The important thing is not that you solve THIS problem, but that you add to your repertoire of logic skills.

In a problem like this, you see several statements that tell you what is not possible, where a vegetable is not located. This suggests that you’ll solve by process of elimination.

How should we start? Shall we start a list of vegetables? (many people forget about the corn listed in the directions). A list of conditions? Or just dive into the first statement. Let's look at them one at a time.

1. 1  The beets and broccoli were planted in opposite corners of the garden; the broccoli plot borders more other plots than the beet plot does.


What do we learn from this statement?  What specific conditions does it contain?

Plots can be distinguished by their number of neighbors and whether or not they’re corners. I count 4 corners and three interior plots. Two bottom corners, D and G border only two neighbors. B,E and F all border 4, while A and C border 3.
 

A. Corner                     Has 3 neighbors		B. Not a corner Has 4 neighbors		C. Corner    Has 3 neighbors
D. Corner Has 2 neighbors	E. Not a corner          Has 4 neighbors		F. Not a corner      Has 4 neighbors		G. Corner Has 2 neighbors


 
 

2. 2 The cabbage and peas plots each border the same number of plots, but the cabbage plot is bigger than the peas plot.


Plots can also be distinguished by their size. The top row of plots are larger than the bottom row. D and G have same size and number of neighbors. A and C are similarly mirrored. But B is bigger than E and F while having the same number of borders so CABBAGE must be in B. Peas could be in E or F but no other.

3. 3 The two root vegetables, beets and carrots, don’t border each other, and neither do the two legumes, peas and beans.


This gives us some good negative information which we can jot down inside the plots.

4. 4 The first letter of at least one vegetable is the same as the label of the plot it’s in.

We’re doing great so far. Let’s go back to the beginning. With what we now know, we’ll get more out of reading them a second time.

1. 1  The beets and broccoli were planted in opposite corners of the garden; the broccoli plot borders more other plots than the beet plot does.

1. 3  The two root vegetables, beets and carrots, don’t border each other, and neither do the two legumes, peas and beans.

Condition 3 also tells us that peas and beans can’t border each other. That means Peas can’t occupy E, which puts them in F, which forces beans into D, leaving carrots in E.

Before we finish, let’s check to make sure all conditions have been met.
 

A. Broccoli		B. Cabbage		C. Corn
D. Beans	E. Carrots		F. Peas		G. Beets