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Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2024 All-Russian Olympiad Regional Round
10.10
10.10
Part of
2024 All-Russian Olympiad Regional Round
Problems
(1)
Graph with knights and liars
Source: ARO Regional stage 2024 10.10
2/2/2024
There are
2024
2024
2024
people, which are knights and liars and some of them are friends. Every person is asked for the number of their friends and the answers were
0
,
1
,
…
,
2023
0,1, \ldots, 2023
0
,
1
,
…
,
2023
. Every knight answered truthfully, while every liar changed the real answer by exactly
1
1
1
. What is the minimal number of liars?
combinatorics