[bonanova]

Suppose three intersecting rectangles are drawn in a plane.

How can they be arranged to produce the largest number of areas enclosed by their sides, not further subdivided?

Example: The figure shows three rectangles A, B and C, that create seven such areas:

1. A B C
   
2. A B C
   
3. A B C
   
4. A B C
   
5. A B C
   
6. A B C
   
7. A B C
   

The area marked 8 is NOT included; not being bounded by the sides of the rectangles.

[Guest]

Suppose three intersecting rectangles are drawn in a plane.

How can they be arranged to produce the largest number of areas enclosed by their sides, not further subdivided?

Example: The figure shows three rectangles A, B and C, that create seven such areas:

1. A B C
   
2. A B C
   
3. A B C
   
4. A B C
   
5. A B C
   
6. A B C
   
7. A B C
   

The area marked 8 is NOT included; not being bounded by the sides of the rectangles.

I can get 19.

Edited March 9, 2009 by BLAHMASTER

[Guest]

I am prob wrong but I got 21

[Guest]

I can see a way to do 13.

If you lay 3 long narrow rectangles across each other so that each rectangle crosses the other two, and so that both ends further stick out, you get 13 areas. I tried to draw it out here:

Edit: Put GIF instead of BMP

Edited March 9, 2009 by jb_riddler

[Guest]

ok i have no clue how to work the attachment thing but

22

[Guest]

I get 24+1 = 25

[Guest]

ok, still trying to figure out attachment

23- one rectangle long side down and two diagonal rectangles that make a pentagon outside of the first rectangle

__ctangle_riddle.htm

Edited March 9, 2009 by outdoorsman

[Guest]

Suppose three intersecting rectangles are drawn in a plane.

How can they be arranged to produce the largest number of areas enclosed by their sides, not further subdivided?

Example: The figure shows three rectangles A, B and C, that create seven such areas:

1. A B C
   
2. A B C
   
3. A B C
   
4. A B C
   
5. A B C
   
6. A B C
   
7. A B C
   

The area marked 8 is NOT included; not being bounded by the sides of the rectangles.

25 - although it is surprisingly hard to count them!

[Guest]

I Got 25 which i think is the maximum possible. To get more such areas one has to go on adding rectangles and overlaping with the previous one such that each side of the rectangle cuts maximum possible lines. Its more clear here:

Each side of the second rectangle cuts 2 lines which is the maximum possible cut, and each side of the third rectangle cuts 4 lines, which is also the maximum possible cut. So, by simple logic I think 25 is the maximum possible no. of such areas.

[Guest]

Kudos to xucam and the-genius. I didn't think of the wreath approach until I was on the way home for the day.

6 red, 6 blue, 12 purple, 1 green = 25

[bonanova]

Inclusion for the 3 rectangles is 3 in one, 3 in two and 1 in all three.

These are shown in the OP pic.

Using the pinwheel configuration,

The two groups of 3 can be replicated on the four sides [24 regions]

The single group of 1 cannot per replicated [1 region]

25 is the max number of regions.