Alice and Bob have been given a composite number N. In each move, a player writes down a composite divisor of N on the board such that there are no two numbers on the board that divde each other or no two numbers that are co prime. Alice plays first. The player who cannot make a move looses Who has the winning strategy? (The book i am solving has a hint that Alice has the winning strategy but that makes no sense to me. Shouldn't it depend on what is N. A counterexample is N= p^2. N is composite and alice cannot make a move since N has no composite divisors. Similarily you can prove that in p1p2 Bob has a winning strategy. Am i misunderstanding the question?)
#Combinatorial game theory
sharp dome
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Alice and Bob have been given a composite number N. In each move, a player write...
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rugged patrol
Alice and Bob have been given a composite number N. In each move, a player write...
It's possible you haven't described the problem totally accurately.
sharp dome
It's possible you haven't described the problem totally accurately.
wait I'll share the screenshot
okay
The number N is the product of k diferent primes (k ≥ 3). Two
players play the following game. In turn, they write composite divisors of N on a blackboard. One may not write N. Also, there may
never appear two coprime numbers or two numbers, one of which
divides the other. The first player unable to move loses. Does the
first player or the second player have a winning strategy?
sharp dome
The number N is the product of k diferent primes (k ≥ 3). Two
players play the f...
This was the problem statement from the original source.
and there was a gross printing mistake in the description of the same problem in the book i was using
fuck
they didn't inlcude the fact that N is product of k different primes
The book i am using is quite new. It was published in 2025
or maybbe 2024
grave lark
rugged patrol
wait I'll share the screenshot
...where's the screenshot?
sharp dome
Its alright
theres no point in sending the screenshot when I know that problem statement is incomplete
sharp dome
The number N is the product of k diferent primes (k ≥ 3). Two
players play the f...
This is original completely problem statement i found in the original source, copy pasted as it is.
tame stag
This is original completely problem statement i found in the original source, co...
Hello, are you studying combinatorial game theory? I am too. May I dm you (or you dm me). Perphabs we could help each other
Also are you doing this recreationally or for school?
Also also, how good are you at this. Im not exactly the sharpest tool in the shed and I dont wanna waste your time if a. This is for school or b. You are already way more well versed than me
sharp dome
Also are you doing this recreationally or for school?
Also also, how good are ...
its school level
I am studying for context math
*contest
alpine rampart
The number N is the product of k diferent primes (k ≥ 3). Two
players play the f...
For the case k = 3, Alice would win because there are 3 possibilities for composite divisors which aren't coprime and aren't multiples of each other
for example N = pqr
the divisors are pq, qr, pr
cold topazBOT
@sharp dome