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Kürschák Math Competition
1948 Kurschak Competition
1948 Kurschak Competition
Part of
Kürschák Math Competition
Subcontests
(3)
3
1
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among any n positive integers one can always find some such n| their sum
Prove that among any
n
n
n
positive integers one can always find some (at least one) whose sum is divisible by
n
n
n
.
2
1
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convex polyhedron with no diagonals is a tetrahedron
A convex polyhedron has no diagonals (every pair of vertices are connected by an edge). Prove that it is a tetrahedron.
1
1
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more frequent for New Year's Day, Sunday or Monday
Knowing that
23
23
23
October
1948
1948
1948
was a Saturday, which is more frequent for New Year’s Day, Sunday or Monday?