Question

IF U ANSWER 1 OF THESE QUESTIONS, I WILL ADD U BRAINLIEST

The points in a 55 square array are each coloured either blue or yellow.
Show that there must be four points of the same colour that form a rectangle whose sides are
parallel to the sides of the array.
3. A mathematics teacher wrote the quadratic x 2 + 10x + 20 on the board. Then each student,
in turn, either increased by 1 or decreased by 1 either the constant or the linear coefficient.
Finally, x 2 + 20x + 10 appeared. Did a quadratic with integer roots necessarily appear on the
board at some stage in the process?
4. A convex polygon has 1993 vertices which are coloured so that neighbouring vertices are of
different colours. Prove that one can divide the polygon into triangles with non-intersecting
diagonals whose endpoints are of different colours.

Answer 1

Answer:

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