I can't figure it out any help?

Let n ≥ 1 be an odd integer. Alice and Bob play the following game, taking alternating turns, with Alice playing first. The playing area consists of n spaces, arranged in a line. Initially all spaces are empty. At each turn, a player either

– places a stone in an empty space, or

– removes a stone from a nonempty space s, places a stone in the nearest empty space to the left of s (if such a space exists), and places a stone in the nearest empty space to the right of s (if such a space exists). Furthermore, a move is permitted only if the resulting position has not occurred previously in the game. A player loses if he or she is unable to move. Assuming that both players play optimally throughout the game, what moves may Alice make on her first turn?

#Combinatorics

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
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Comments

i wanna know from where i should start thinking then the proper solution ???

Ahmed Mahmoud - 3 years, 1 month ago

I am not being helpful

Annie Li - 3 years, 1 month ago

just commenting is helpful it means someone pay attention :)

Ahmed Mahmoud - 3 years, 1 month ago

Ha ha. I pay attention to most discussions with an interesting title. Good luck

Annie Li - 3 years, 1 month ago

@Annie Li – thanks

Ahmed Mahmoud - 3 years, 1 month ago

@Ahmed Mahmoud – No problem even tho i did nothing to help give you the answer

Annie Li - 3 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$