okay... perhaps "It's a 2-player game that's deterministic, zero-sum, perfect information, finite, and without ties. So a winning strategy exists for one of the players." should have been mentioned... I didn't know that.
Btw, what is the proof of the statement I just quoted? thanks On Oct 2, 7:25 pm, Geoffrey Summerhayes <[email protected]> wrote: > On Oct 2, 7:20 am, eSKay <[email protected]> wrote: > > > What exactly do you prove here? > > The first player always has a winning move. > > > You just make some statements, which should be proved. shouldn't it? > > > Or am I missing something?? > > It's a 2-player game that's deterministic, zero-sum, > perfect information, finite, and without ties. So a > winning strategy exists for one of the players. > > The proof doesn't indicate what the winning play is > for any given N, just that a winning play always exists > for the first player. > > -- > Geoff > > > On Oct 2, 7:08 am, saltycookie <[email protected]> wrote: > > > > Here is a proof. Unfortunately, the proof is not constructive.The > > > secret of winning is "1", which is a fator of every integer. > > > > If the first player(player A) can win by removing a number between 2 > > > to n, then our hypothesis holds. Or else, A can't win by removing any > > > number between 2 to n. We denote the situation after removing number i > > > from [1, n] by S(n, i), then for i = 2...n, S(n, i) is a winning > > > situation. A can then remove number 1 at the first step. No matter > > > what B removes in the next step, he will leave a situation S(n, i)(i > > > is the number B removes), which is a winning situation for the next > > > player(A). > > > > On 10月1日, 上午2时53分, nikhil <[email protected]> wrote: > > > > > we have all the numbers written from 1- n. 2 players play > > > > alternatively. At any turn , a player removes a number and along with > > > > all its divisors present in the list. Player to remove last number > > > > wins. > > > > > so given initial number n and player who is starting first , we are to > > > > find who wins if both play optimum. > > > > > NOW , i have found that the the player who starts ALWAYS wins. Can > > > > anyone prove this or still better come up with a real strategy ! > > > > > cheers > > > > - > > > > nikhil > > > > Every single person has a slim shady lurking !- Hide quoted text - > > > - Show quoted text - --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/algogeeks -~----------~----~----~----~------~----~------~--~---
