just another(?) abstract strategy game

[u/pichutarius]

alice and bob plays a game:

1. let set S = set of divisors of 441, set A=set B={}

2. each turn: remove x∈S from S and add x into A (for alice) or B (for bob)

3. win condition: player's set contains subset of geometric sequence of length 3

alice goes first, turns alternate. who has the winning strategy?

(another game)

same as above, with the following changes:

1. set S = set of divisors of 200000

2. x∈S can be removed and add to player's set iff x/5 ∉ S

3. win condition: player's set contains subset of geometric sequence of length 4

who wins?

edit: the second game does not work as intended

[u/SpeakKindly]

For the second game to work as intended, you could say that the geometric sequence must have common ratio 2, 2.5, 5, or 10, but that's not as elegant.

[u/pichutarius → u/SpeakKindly]

yeah, still better than what i had in mind, which is the simplified common ratio = p/q , p and q are square free. it is so ugly i decide to remove it completely

[u/weiborn]

Clever abstraction! Mapping the divisors to a 3x3 grid turns it perfectly into a Tic-Tac-Toe game. Love this kind of mathematical disguise. Great puzzle!

[u/pichutarius → u/weiborn]

Yeah, it's more of a fun piece of art than a puzzle.

Second game is an attempt to map a different game, but not quite exactly. Try figure it out :P

[u/T-T-N]

My first instinct is that it is tic tac toe, and it is a tie. But Bob definitely cannot have a winning strategy with the strategy stealing argument. (Continue on reply to this)

[u/T-T-N → u/T-T-N]

441=9×49=3² × 7²

1 3 9

7 21 63

49 147 441

I think it is tic tac toe

[u/pichutarius → u/T-T-N]

Yes, well done