MathDB
Problems
Contests
National and Regional Contests
Netherlands Contests
Dutch Mathematical Olympiad
1982 Dutch Mathematical Olympiad
1982 Dutch Mathematical Olympiad
Part of
Dutch Mathematical Olympiad
Subcontests
(4)
4
1
Hide problems
gcd
Determine \gcd (n^2\plus{}2,n^3\plus{}1) for n\equal{}9^{753}.
3
1
Hide problems
marbles
Five marbles are distributed at a random among seven urns. What is the expected number of urns with exactly one marble?
2
1
Hide problems
construction
In a triangle
A
B
C
ABC
A
BC
,
M
M
M
is the midpoint of
A
B
AB
A
B
and
P
P
P
an arbitrary point on side
A
C
AC
A
C
. Using only a straight edge, construct point
Q
Q
Q
on
B
C
BC
BC
such that
P
P
P
and
Q
Q
Q
are at equal distance from
C
M
CM
CM
.
1
1
Hide problems
easy inequality
Which is greater:
17091982
!
2
17091982!^2
17091982
!
2
or
1709198
2
17091982
17091982^{17091982}
1709198
2
17091982
?