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I am not getting this... Could you give a more thorough explanation please?

If n=16 for example Rita could draw 1, then Sam could draw 5, then Rita could draw 4 leaving 6 sticks, and no matter what Sam draws next she would have last picks.

I don't see the point in adding 1+2+3+4+5 since each player can decide the number of sticks to retrieve from the pack in each draw. For example Sam could draw 1 stick every time... or 5 sticks every time he draws...

If Rita goes 1st, and there are 12 sticks:
She takes one, sam takes 5, leaves her with 6
she takes 2, sam takes 4, sam leaves her with 6
she takes 3, sam takes 3, sam leaves her with 6
she takes 4, sam takes 2, sam leaves her with 6
she takes 5, sam takes 1, sam leaves her with 6.

if she is left with six, she will leave sam with five or fewer. Sam will win.

the basic assumption you should take in the ques is "sam win whatever rita plays"...sam will make his moves depending on what rita does...he will not play a random game...

until and unless it is specified that "sam's play doesn't depend on rita's play" if I consider this case .... hmmm....I didn't get an answer.

I agree with u explaination - because that is how I visualized it and I will stop bugging ppl more with my posts - because I am gonna confuse myself even further.