be a triangle inscribed in circle 
,
and 
intersect 
and 
respectively. Let 
be the center of the circle through 
at 
be the center of the circle through 
at 
is a connected graph with 
edges. Prove that it is possible to label the edges 
in such a way that at each vertex which belongs to two or more edges, the greatest common divisor of the integers labeling those edges is equal to 1.
belongs to at most one edge. The graph 
is connected if for each pair of distinct vertices 
there is some sequence of vertices 
such that each pair 
is joined by an edge of 
.
of positive real numbers,
.
Y by
Let 
be a positive integer and consider the set 
.
Two players alternate moves. On each turn, the current player must select a nonempty subset
of numbers not previously chosen such that for every distinct 
, neither 
divides 
nor divides .
After selecting
, all multiples of every element in , including those in itself, are removed from 
.
The game continues with the reduced set until no moves are possible.
Determine, for each, which player has a winning strategy if any
Note: It might be wrong or maybe too easy.
be a positive integer and consider the set 
.Two players alternate moves. On each turn, the current player must select a nonempty subset
of numbers not previously chosen such that for every distinct 
, neither 
divides 
nor divides .After selecting
, all multiples of every element in , including those in itself, are removed from 
.The game continues with the reduced set
until no moves are possible.Determine, for each
, which player has a winning strategy if anyNote: It might be wrong or maybe too easy.
This post has been edited 1 time. Last edited by JARP091, May 24, 2025, 5:30 AM
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