Can you please answer asap using graph to show method and st

Can you please answer asap using graph to show method and strategy

Note: the number of matches in pile are n. And we want to put the next player in a losing position.

Please show strategy i.e., the multiple that put the player in a losing position.

Let N be the matchstick,left in pile, on my turn.

So if N=1,2,5, I will win the game,if N=3, I will loose whatever , i will choose.

if N=4, I will choose 1 matchstick , next person has to pick from 3 mathstick, so I will win.

as gcd(2+1,1+5)=3

If N is multiple of 3 then i will certainly loose.

So the good strategy would be to pick \"i\" matchstick such that N-i is divisible by 3.i=1,2,5