2

Part of 1974 Bundeswettbewerb Mathematik

Problems(2)

Bundeswettbewerb Mathematik 1974 Problem 1.2

Source: Bundeswettbewerb Mathematik 1974 Round 1

Seven polygons of area

1

lie in the interior of a square with side length

2

. Show that there are two of these polygons whose intersection has an area of at least 1\slash 7.

geometryareapolygonsquare

Bunndeswettbewerb Mathematik 1974 Problem 2.2

Source: Bundeswettbewerb Mathematik 1974 Round 2

30

apparently equal balls,

15

of which have the weight

a

and the remaining

15

have the weight

b

a \ne b

. The balls are to be partitioned into two groups of

15

, according to their weight. An assistant partitioned them into two groups, and we wish to check if this partition is correct. How can we check that with as few weighings as possible?

combinatoricsweighing