## Farmer Land Tree Division

A farmer at his death left a field containing 12 trees planted as shown below, and commanded in his Will that each of his 4 sons should have an equal share of land and an equal number of trees.

How was it divided?

*(will unmask any submitted answers on Friday)*

Shawn| PUZZLE GRANDMASTER | Profile December 12th, 2007 - 2:06 pm1. Draw a horizontal line 1/4 of the way up from the bottom of the drawing

2. Draw a horizontal line 3/4 of the way up from the bottom of the drawing

Shawn| PUZZLE GRANDMASTER | Profile December 12th, 2007 - 2:08 pmOops, hit the wrong button!!

3. In the middle area, draw a vertical line down the exact middle

4. Each of 4 areas has 3 trees inside.

5. The top and bottom areas measure (1)x(1/4) = 1/4 square widgets

6. The middle areas measure (1/2)x(1/2) = 1/4 square widgets

Gray-T| Profile December 12th, 2007 - 5:27 pmC´mon that´s easy.

Did you ever read Ulysses by Homer, not Simpson, in Old Greak? That would really puzzle you…

But here is some other puzzle, I suggest:

I have a black hole in my right, a Ring in my left, my feets are free, but save and private, sometimes pirate, but never mean.

May head stood always the same, for the right person to see.

Who am I, and who is my Queen?

Some clue: Stars are just Holes in Black Velvet Sheets…

And if it´s velvet, we will see…

suineg| PUZZLE MASTER | Profile December 13th, 2007 - 9:54 amIf they can share a tree, then if you divide he triangle by his 2 diagonals, you have the same area and every diagonal has 1 tree, so each one of the sons has 4 trees, because they share half of tree with each one of his adyacent brothers

suineg| PUZZLE MASTER | Profile December 13th, 2007 - 9:58 amI correct my self, you divide the square by his two diagonals you get 4 triangles with the same area, each side of the traingles wich is not his a side of the original square has a tree, so each brother share a tree with his adyacent brother, half and half, 2 + 1/2+!/2= 3 trees, each brother has 3 trees

suineg| PUZZLE MASTER | Profile December 13th, 2007 - 10:07 amwell maybe its not like that, let me think it more, because i think theres a flaw, one area gets one tree more

suineg| PUZZLE MASTER | Profile December 13th, 2007 - 10:16 amok, now my definitive answer:

A: length of a side of the square

square divide in 4 sections:

1) up : three tress in line, a rectangle of area A * A/4

2) middle: two squares with three trees in form of atip of a n arrowe, with an area of A/2*A/2

3) down: same as up

slavco23| Profile December 13th, 2007 - 10:55 amhttp://i41.photobucket.com/alb.....edland.jpg

Megan W| Profile December 14th, 2007 - 12:13 amOf course, the most obvious way to divide the land would be to draw 2 lines: one down the center vertically, and one horizontally – but I’m not sure anyone would approve of halving any trees!

SO the correct way to divide them up then would be to draw lines horizontally both 1/4 and 3/4s of the way down the side of the map (all the way across the image) and then a line down the center vertically of the map – but only between the lines already drawn!

This way, each boy has exactly 3 trees each, and 1/4 of the land Easy

P.S I hope I explained that clearly!

foger1979| Profile December 14th, 2007 - 4:08 pmIf you divide the farm into a 4×4 square, then each one gets a plot of land in the shape of a “t”. Each of the four kids gets 3 trees.

foger1979| Profile December 14th, 2007 - 4:10 pmI have posted an attempt at a diagram.

http://img40.picoodle.com/img/.....f13caf.png

White Rabbit| Profile December 14th, 2007 - 8:23 pmThe top of the “field” is 6 trees wide (width), the edge of the field is 4 trees wide (hight). One person gets the three trees at the top (V) with a piece of land 1 tree thick and 6 trees wide he gets 3 trees and piece of land that is 6 trees^2. Same thing for the bottom 3 trees (U). The other two ppl get 3 trees in the center (O or T) and a piece of land 3 trees thick and 2 trees wide, so it has an area of 6 trees^2, the same as all the other pieces.

V…..V……V

….O…..T….

O………….T

….O….T…..

U…..U…..U

RK.| Profile December 15th, 2007 - 12:16 pmvery good, most of the answers are as Slavco23 and White Rabbit show in their diagrams. Foger1979 shows another way to do it too

Gray-T: I can’t figure it out. If you wouldn’t mind, maybe I’ll post it Monday evening/Tuesday morning, and remove comment moderation so visitors can try together to solve it in real time…

rmsphoto| Profile December 19th, 2007 - 12:15 pmBasically 2 diamonds that touch at the middle, and each side of the property, around the middle groupings of trees, leaving sawtooth patterns at the top and bottom, so each son gets three trees.

bbtori7| Profile December 22nd, 2007 - 7:02 pmThats so easy!

Its three per boy.

RK| Profile December 24th, 2007 - 1:02 pmsorry, we’re having trouble with the comment system, the original 14 comments are not showing currently. We’re working on a fix, thanks