be the Fermat point of a 
.
,
,
are concurrent and the point of concurrence is 
,
(
well). i want to study so if you guys have some easy or normal problems please send me
?
chess board, except for the 
central square, there is a checker. In one move, a checker can jump over adjacent checker (diagonally), and this adjacent checker (that was jumped over) is removed. Is it possible to come up with a sequence of moves, so that only one checker is left on the board?
Y by
At a chess tournament, every pair of contestants played each other at most once. If any two con-
testants,
and 
, failed to play each other, then exactly two other contestants, 
and 
, played
against both and during the tournament. Moreover, no 
contestants played exactly 
games
between them. Prove that every contestant played the same number of games.
Authored by Mirko Petrushevski
testants,
and 
, failed to play each other, then exactly two other contestants, 
and 
, playedagainst both
and during the tournament. Moreover, no 
contestants played exactly 
gamesbetween them. Prove that every contestant played the same number of games.
Authored by Mirko Petrushevski
This post has been edited 2 times. Last edited by steppewolf, Feb 9, 2025, 10:40 PM
play each other. Now we have that whenever there is an edge 
in the graph, there is also an edge 
such that 
,
,
and 
aren't connected with edges. Call such pairs of edges 
.
.
which is an endpoint of the conjugate of an edge 
.
of 
is an edge, or 
.
has maximal degree, and now we can prove every vertex has maximal degree using breadth first search, since the graph is connected.
