Kilayim 3:6 poses the case of a field sown with onions, and one wishes to plant gourds in this field. There are three opinions as to how much one should uproot, and as they pose their opinions in very cryptic wordings, I will explain their opinions according to the Rambam, Bartenura, and Tiferes Yisrael, who all seem to agree on how the Mishnah should be read.
R' Yishmael says one should make alternating patches of 8 amos filled with the onions and 8 amos left fallow, then plant the gourds in the center 4 amos of the 8-amah fallow patches. This leads to an alternating pattern of 8 amos of onions, 2 amos fallow, 4 amos of gourds, and 2 amos fallow.
R' Akiva says that you don't need 2 amos fallow between the onions and gourds; you can just plant a row of flax (a minimal width) between them. Thus, the pattern is 8 amos onions, tiny little immeasurable gap, 8 amos gourds, tiny little immeasurable gap.
The Chachamim say that R' Yishmael is correct in that there must be 12 amos between patches of gourds (in R' Yishmael's view, that was 4 amos fallow and 8 amos of onions), but they agree with R' Akiva that you don't need 2 amos between the differing species. Thus, the gourds are still four amos wide, but the onions can be expanded to 12 amos.
My question is: Why do the fields need to alternate?
Let's take a field of 52 amos wide. According to R' Yishmael, we begin with 4 amos of gourds, then a 2 amah gap, then 8 amos of onions, then a 2 amah gap; this pattern repeats two times, followed by one last four-amah field of gourds. This is a total of 16 amos of gourds, and 24 amos of onions.
If he simply requires that there be two amos between the gourds and onions, let the 24 amos of onions remain constant, add a 2-amah gap, and then plant the remaining 26 amos of field with gourd. By not alternating fields, he gains 10 amos of gourds!
(According to R' Akiva and the Chachamim, where no gaps are lost by not alternating, this suggestion would have no impact on their opinions.)
