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National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
2001 Switzerland Team Selection Test
9
9
Part of
2001 Switzerland Team Selection Test
Problems
(1)
16 secret agents in Geneva
Source: Switzerland - Swiss TST 2001 p9
2/18/2020
In Geneva there are
16
16
16
secret agents, each of whom is watching one or more other agents. It is known that if agent
A
A
A
is watching agent
B
B
B
, then
B
B
B
is not watching
A
A
A
. Moreover, any
10
10
10
agents can be ordered so that the first is watching the second, the second is watching the third, etc, the last is watching the first. Show that any
11
11
11
agents can also be so ordered.
combinatorics