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Problems
Contests
National and Regional Contests
Hungary Contests
Kürschák Math Competition
1947 Kurschak Competition
1947 Kurschak Competition
Part of
Kürschák Math Competition
Subcontests
(3)
3
1
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min no of disck radius 1/2 to cover a disk of radius 1
What is the smallest number of disks radius
1
2
\frac12
2
1
that can cover a disk radius
1
1
1
?
2
1
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any graph with 6 points has a triangle or 3 points not joined to each other
Show that any graph with
6
6
6
points has a triangle or three points which are not joined to each other.
1
1
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46^{2n+1} + 296 x 13^{2n+1} is divisible by 1947
Prove that
4
6
2
n
+
1
+
296
⋅
1
3
2
n
+
1
46^{2n+1} + 296 \cdot 13^{2n+1}
4
6
2
n
+
1
+
296
⋅
1
3
2
n
+
1
is divisible by
1947
1947
1947
.