Farmland Maths problem

[TeacherArm92]

Can anyone solve this question below:

It appeared on a KS2 scheme of work. There were no answers included. I've managed to solve the earlier easier ones but the last one has proven tricky.

A farmer has to will his house and ponds to his 3 sons and 1 daughter. Each farm must have 1 house and 1 pond. Each farm must be the same shape and have the same area. Here are the answers to some easier questions. See if you can solve the last one.

 

[stapel]

Can anyone solve this question below:

Probably. But we're here to help *you* solve it, not to solve it for you.

There were no answers included. I've managed to solve the earlier easier ones but the last one has proven tricky.

A farmer has to will his house and ponds to his 3 sons and 1 daughter. Each farm must have 1 house and 1 pond. Each farm must be the same shape and have the same area. Here are the answers to some easier questions.

From the second and third images posted, would it be correct to gather that some of the farmer's land may be left to charity, or to some party other than his four kids?

Thank you!

 

[TeacherArm92]

Probably. But we're here to help *you* solve it, not to solve it for you.


From the second and third images posted, would it be correct to gather that some of the farmer's land may be left to charity, or to some party other than his four kids?

Thank you!

Yes farmland can be left over.

 

[Dr.Peterson]

Can anyone solve this question below:

It appeared on a KS2 scheme of work. There were no answers included. I've managed to solve the earlier easier ones but the last one has proven tricky.

A farmer has to will his house and ponds to his 3 sons and 1 daughter. Each farm must have 1 house and 1 pond. Each farm must be the same shape and have the same area. Here are the answers to some easier questions. See if you can solve the last one.

These are what I would call puzzles, for which there is no particular method other than perseverance. They are not easy.

Since you didn't use all the space in your answers 2 and 3, they are wrong by my interpretation of the problem. How much area should each person get?

The last one, however, I solved easily. Since the outer corners are to be assigned to different people, something like a spiral seems like a good idea, and it will work.

I haven't solved 2 and 3 yet, though. Give those another try. (And it may help if you show us the originals of those, without faulty solutions.)

 

[Steven G]

I would 1st do some long division to determine how much land each person would get. Then I would try to solve the puzzle.
I doubt that land can be left over. At least, it doesn't have to be that way.

 

[Dr.Peterson]

Yes farmland can be left over.

Is that explicitly stated? Can you show the entire wording, or other examples that demonstrate what is intended (by showing answers that leave space unused)?

That is not allowed in problems of this genre that I have seen (dissection problems). And I have now solved them without leaving anything unused. (Hint: they all have some sort of symmetry, like the first one, but not all the same.)

 

[TeacherArm92]

Using your advice I've redone the second puzzle so all squares are used. This is the previously posted 3rd puzzle with no marks on it.

 

[blamocur]

The last one makes me think of spiral shapes.

 

[Dr.Peterson]

Using your advice I've redone the second puzzle so all squares are used. This is the previously posted 3rd puzzle with no marks on it.


View attachment 36012

Thanks; this was the hardest one to read, and to process so I could work on it. It was probably also the hardest to solve.

Now, have you tried something sort of spiralish for this one, too? I can't really give any good hints without giving it away. (And you do want to learn for yourself how to do the thinking, right?)

I wasn't aiming for a spiral as I worked it out, but just tried something to connect the upper left pair, while thinking about what the others would need. But the four Hs in the middle do suggest a spiral symmetry, now that I think about it.

Can you show us your answer for the second? That's the only one for which my answer doesn't have rotational symmetry.

 

[Dr.Peterson]

Here's one way you might start the third: pair up which H and P might go together (in order to allow non-crossing paths between them):

​

You could even guess that the corners are similarly assigned, supposing that the answer is a sort of spiral:

​

Then try filling in between, making the shapes congruent.

 

[stapel]

Here's one way you might start the third: pair up which H and P might go together (in order to allow non-crossing paths between them):

View attachment 36032​

You could even guess that the corners are similarly assigned, supposing that the answer is a sort of spiral:

View attachment 36031​

Then try filling in between, making the shapes congruent.

Nice! ?