Posted by **Tyler** on Thursday, April 15, 2010 at 3:53am.

Suppose 100 dots are arranged in a square 10 × 10 array, and each dot is colored red

or blue.

(a) Prove that this array must contain a “monochromatic” rectangle. That is, no matter

how the red and blue colors are assigned, there must be either a set of four red dots that

form a rectangle or else a set of four blue dots that form a rectangle.

[Don’t consider colors of the dots inside that rectangle. Just the four corner points.

Use only those rectangles having horizontal and vertical sides. ]

(b) Does this result remain true for smaller rectangular arrays of dots?

To begin, find a 4 × 5 array that admits no monochromatic rectangle.

Must a monochromatic rectangle exist in a 5 × 5 array? In a 4 × 6 array?

- math -
**sss**, Sunday, March 6, 2016 at 12:17am
qweqwe

## Answer This Question

## Related Questions

- Math - Consider a rectangular array of dots with an even number of rows and an ...
- math - Consider a rectangular array of dots with an even number of rows and an ...
- math array - my grandaughter is doing array dot to dot sample make as ...
- math - On the plant ZOG,colored coins are used formoney. Suppose 12 white, 9 red...
- Biology - Two purple flowers (Bb) are bred with each other in the same garden. ...
- College Finite Math - Your Open QuestionShow me another » If the ball is either ...
- Maths - Mary has 6262 square blue tiles and a number of square red tiles. All ...
- math - A bag contains red, blue, and orange marbles. If the probability of ...
- STATISTICS - There are 10 colored balls in a box ( 5 red, 3 blue, 2 green ). ...
- STATISTICS - There are 10 colored balls in a box ( 5 red, 3 blue, 2 green ). ...

More Related Questions