be an acute triangle. Points 
,
lie on a line in this order and satisfy 
.
and 
be the midpoints of 
and 
,
is acute, and let 
be its orthocentre. Points 
and 
lie on lines 
and 
,
and 
and 
and 
such that 
of positive integers is called central if for every positive integer 
,
terms of the sequence is equal to 
of positive integers such that for every central sequence 
,
.
Y by
Andrew and Barry play the following game: there are two heaps with 
and 
pebbles, respectively. In the first round Barry chooses a positive integer 
and Andrew takes away 
pebbles from one of the two heaps (if is bigger than the number of pebbles in the heap, he takes away the complete heap). In the second round, the roles are reversed: Andrew chooses a positive integer and Barry takes away the pebbles from one of the two heaps. This goes on, in each round the two players are reversing the roles. The player that takes the last pebble loses the game.
Which player has a winning strategy?
Submitted by András Imolay, Budapest
and 
pebbles, respectively. In the first round Barry chooses a positive integer 
and Andrew takes away 
pebbles from one of the two heaps (if is bigger than the number of pebbles in the heap, he takes away the complete heap). In the second round, the roles are reversed: Andrew chooses a positive integer and Barry takes away the pebbles from one of the two heaps. This goes on, in each round the two players are reversing the roles. The player that takes the last pebble loses the game.Which player has a winning strategy?
Submitted by András Imolay, Budapest
or 
or 
or 
or 
or 
or 
Andrew wins.Otherwise Barry wins.
