2005 Taiwan TST Round 1

Part of TST Round 1

Subcontests

(3)

2

Tournament

n

teams take part in a tournament, in which every two teams compete exactly once, and that no draws are possible. It is known that for any two teams, there exists another team which defeated both of the two teams. Find all

n

for which this is possible.

gcd and lcm

Find all positive integer triples

(x,y,z)

x<y<z

\gcd (x,y)=6

\gcd (y,z)=10

\gcd (x,z)=8

(x,y,z)=2400

. Note that the problems of the TST are not arranged in difficulty (Problem 1 of day 1 was probably the most difficult!)

5

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