Wednesday

July 23, 2014

July 23, 2014

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

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?

**Related Questions**

math array - my grandaughter is doing array dot to dot sample make as ...

making dot arrays - to make a 14-dot array that has exactly two rows, is this ...

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 - don break a 4x7 array into a 2x7 array and another array. what is the ...

dot array - on centameter dot array draw all possible rectangles with a ...

Math - Don breaks a4 by 7array into a 2 by 7 array and another array. What is ...

Array - what do you call the numbers that cannot be arranged into 2-row array? I...

college - Write a C++ program to fill an array with 6 numbers, and then reverse...

dot array - centimeter dot array draw all possible rectangles with the area of ...