math

posted by .

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 -

    qweqwe

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    A bag contains red, blue, and orange marbles. If the probability of randomly selecting a red marble is 0.4 and the probability of selecting a red or blue marble is 0.9 what is the probability of selecting a red or orange marble?
  2. math

    On the plant ZOG,colored coins are used formoney. Suppose 12 white, 9 red, 8 yellow, 4 blue, and 0 green can be exchanged for 2 white, 1 red, 0 yellow, 1 blue ,and 1 green. Also, suppose 1 green = N blue, 1 blue = N yellow, 1 yellow …
  3. College Finite Math

    Your Open QuestionShow me another » If the ball is either blue or white, what is the probability that it was drawn from urn Y?
  4. math array

    my grandaughter is doing array dot to dot sample make as manydifferent arrays as possible number 5 how would i go about doing a array with dots please, desperate in need to keep up with my grandaughters homework.
  5. math

    Consider a rectangular array of dots with an even number of rows and an even number of columns. Color the dots, each one red or blue, in such a way so that in each row half the dots are red and half are blue, and also in each column …
  6. Math

    Consider a rectangular array of dots with an even number of rows and an even number of columns. Color the dots, each one red or blue, in such a way so that in each row half the dots are red and half are blue, and also in each column …
  7. STATISTICS

    There are 10 colored balls in a box ( 5 red, 3 blue, 2 green ). What is the probability of picking out a red ball and then a blue ball ( If I do not replace the red ball
  8. STATISTICS

    There are 10 colored balls in a box ( 5 red, 3 blue, 2 green ). What is the probability of picking out a red ball and then a blue ball ( If I do not replace the red ball )?
  9. Biology

    Two purple flowers (Bb) are bred with each other in the same garden. What are the odds that red (BB) and blue (bb) flowers will occur in the second generation?
  10. Maths

    Mary has 6262 square blue tiles and a number of square red tiles. All tiles are the same size. She makes a rectangle with red tiles inside and blue tiles on the perimeter. What is the largest number of red tiles she could have used?

More Similar Questions