IMO Shortlist 1983 problem 13
Kvaliteta:
Avg: 0,0Težina:
Avg: 0,0 Let
be the set of
points of the space
all three of whose coordinates are integers between
and
(including
and
). A coloring of
is a map from
to the set {red, blue}. How many colorings of
are there satisfying the following property: The number of red vertices among the
vertices of any right-angled parallelepiped is a multiple of
?
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
![1983^3](/media/m/4/b/9/4b96f964c6c2f0b70de11ea64cb4c749.png)
![\mathbb R^3](/media/m/e/5/8/e58f130e754210706d85a55e4695123a.png)
![0](/media/m/7/b/8/7b8b0b058cf5852d38ded7a42d6292f5.png)
![1982](/media/m/3/8/3/38305100eeadb6d4275e67d70ddc48ff.png)
![0](/media/m/7/b/8/7b8b0b058cf5852d38ded7a42d6292f5.png)
![1982](/media/m/3/8/3/38305100eeadb6d4275e67d70ddc48ff.png)
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
![8](/media/m/3/d/2/3d2c45264dbff498f9bcb16af5f83881.png)
![4](/media/m/d/a/6/da6087359ae47e86dcb2e49565050046.png)
Izvor: Međunarodna matematička olimpijada, shortlist 1983