# Find the empty plot of land

Each of 4 brothers (Yellow, Green, Brown, and Red) has 5 rectangular plots of land. Land plots are numbered 1 to 21 in the diagram below. One of the plots is empty (not owned by any of the brothers).

Each brother's land plots are orthogonally connected to his other land plots. To be "by" something means orthogonally OR diagonally connected. Ex.: 8 land plots are "by" the pond.

Questions
1. If the empty plot must be by the plots of a single (not more than one) brother, which land plot(s) can it be?
2. If the empty plot must be by the plots of multiple brothers' plots, which land plot(s) can it be?

Single Brother: it may be in the plot 1 as my picture shows, or plot 11 as showed earlier by Aify.

Double brother: 8 as Aify showed.

Single brother:

11 (or 1 if you shift the 2 yellow plots beside the house down by 1)

Multiple brothers:

8 - it's beside 2 brothas!

Edit: As noted by OP, this answer was incomplete because it's missing all the possible configurations. It has now been edited to include the other possible configuration.

In the diagram below, the light blue represents the 2 possible empty spots. The brown spot and the empty spot can be interchanged without breaking any rules.

• Great answer. So close, but not quite complete. – JLee Mar 18 '15 at 13:09
• @JLee why is it not complete? – Aify Mar 18 '15 at 16:43
• See the accepted answer – JLee Mar 18 '15 at 16:47
• @JLee I did, but that doesn't tell me why mine is incomplete - it just shows that there are multiple valid solutions to your puzzle – Aify Mar 18 '15 at 16:48
• Reread the question. I included the (s) on the word plot, which asks for all of them. – JLee Mar 18 '15 at 16:51

I believe that if an empty plot is by only one brother then

it must be by red and is either plot 16 or plot 21.

And that if an empty plot is by multiple brothers then

it must be plot 17 and is either by red brown and green or by brown and green.

• Please post the color configurations if possible. – JLee Mar 18 '15 at 13:03