# How to find the layout of the plots?

A peasant had a square garden of $100 × 100$ meters divided into $100$ equal square plots. In the testament, he left to each of his $7$ male grandchildren a connected region of $10$ plots, forming each of the $7$ batches the same figure. He also left to each of his $3$ female grandchildren a connected region of $10$ plots, and each of the three regions had the same figure, but that figure was different from the boys' one. Moreover, the girl's regions didn't touch two to two, that is, a girl's plot couldn't be contiguos to another girl's one. Find the layout.

Two mirror-symmetrical figures are considered equal.

I don't know how to approach this problem, and I wanted to know if there are special strategies to get started.

I found this exercise in a question from Yahoo Answers that did not have any correct answer. I tried to answer it but I couldn't. It was in Spanish language: https://mx.answers.yahoo.com/question/index?qid=20151205035648AAm4F9l

• Thank you for passing along a fun spatial puzzle! Looks like a good candidate for a dissection tag while seeing how long this takes to solve but in the meanwhile the puzzle statement probably should mention where this puzzle came from.
– humn
Sep 15, 2017 at 22:35
• Does "The three girls' grounds were not contiguous" mean that no two touch or that they don't all three touch one another? And when the boys' plots are described as "contiguous" does it mean that each one is a connected region, or that in some fashion they touch one another? (Clearly they can't all pairwise touch.) Sep 15, 2017 at 22:56
• For both boys and girls, their inherited territory is a connected region of $10$ plots. For a girl, her territory cannot touch the another girl's territory, but two or more boys' territories can. Sep 16, 2017 at 1:30
• I found this exercise in a question from Yahoo Answers that did not have any correct answer. I tried to answer it but I couldn't. It was in Spanish language, and there the asker did not specify the origin either. Should I put this information in the question or the link to the other site? Sep 17, 2017 at 0:20
• As the source is a Yahoo site, it is probably safe to link it within the question itself, regardless of language. (Others may have a more informed opinion.) The safest option is to mention the source within the question and also add a comment that contains the link.
– humn
Sep 17, 2017 at 0:38

I might have misunderstood something but I don't see why the following dissection wouldn't work

This solution can also be quite easily guessed from the fact that $2+5=7$ and $2\cdot 5 = 10$.

I do not have enough proof but

I believe there is no solution to this unique problem.

Here is an attempt:

Oranges are girls' plot, and whatever connected shape you choose and whereever you put girls' plot, there is no way to put boys' plot.

Let's change girls' plot a bit:

So again the same problem, 3 nonconnected same plot ruin the rest of the other shapes since it is mainly required girls and boys's plot shapes to be different. So I believe

Whatever shape you choose for girls' or boys' plot, you cannot find a proper layout because of the given properties. It is also possible to put this into a code for girls and boys shapes to see there is no answer. Because there are limited shapes for boys and girls and there are limited places to put them all.