1

Part of 2021 May Olympiad

Problems(2)

Split in sum groups

Source: May Olympiad 2021 L2 #1

On a board the numbers

1,2,3,\dots,98,99

are written. One has to mark

50

of them, such that the sum of two marked numbers is never equal to

99

100

. How many ways one can mark these numbers?

distance between collinear points (2021 May Olympiad L1 p1)

Source:

In a forest there are

5

A, B, C, D, E

that are in that order on a straight line. At the midpoint of

AB

there is a daisy, at the midpoint of

BC

there is a rose bush, at the midpoint of

CD

there is a jasmine, and at the midpoint of

DE

there is a carnation. The distance between

A

E

28

m; the distance between the daisy and the carnation is

20

m. Calculate the distance between the rose bush and the jasmine.