Optimal strategy -- Tolvunarfraedi2-04

[ Show ]

Support VoyForums

[ Shrink ]

VoyForums Announcement: Programming and providing support for this service has been a labor of love since 1997. We are one of the few services online who values our users' privacy, and have never sold your information. We have even fought hard to defend your privacy in legal cases; however, we've done it with almost no financial support -- paying out of pocket to continue providing the service. Due to the issues imposed on us by advertisers, we also stopped hosting most ads on the forums many years ago. We hope you appreciate our efforts.

Show your support by donating any amount. (Note: We are still technically a for-profit company, so your contribution is not tax-deductible.) PayPal Acct: Feedback:

Donate to VoyForums (PayPal):

[ Login ] [ Contact Forum Admin ] [ Main index ] [ Post a new message ] [ Search | Check update time ]

Subject: Optimal strategy

Author:
Hj�lmt�r

[ Next Thread | Previous Thread | Next Message | Previous Message ]

Date Posted: 15:36:59 02/12/04 Thu

�a� kom fram spurning eftir fyrirlesturinn � morgun um heg�un "optimal strategy" a�fer�arinnar til a� spila Nim.
�g svara�i �v� ekki alveg r�tt, �annig a� h�r kemur n�kv�mara svar.

Segjum a� sta�an s� s� a� �rj�r hr�gur s� me� 4, 5 og 2 steina hver. �� er tv�undar�tg�fur �essara talna XOR-a�ar saman:

4: 0100
5: 0101
2: 0010
--------
�tk: 0011

Ef vi� XOR-um �tkomuna vi� hin gildin �� f�um vi� hvert n�ja gildi� � hr�gunni �arf a� vera til a� XOR-unin � �llum gildunum g�fi 0000. �etta n�ja gildi m� au�vita� ekki vera meira en gamla gildi� � hr�gunni, �v� �� urfum vi� a� B�TA vi� steinum, en vi� megum bara taka burt steina.

Sko�um XOR-un �tkomunnar vi� gildi einstakra hr�ga:
Hr�ga 1: 0100^0011=0111, n�ja gildi� er �v� 7, sem er meira en gamla gildi�, sem var 4, svo �etta gengur ekki. Hr�ga 2: 0101^0011=0110, n�ja gildi� er 6, en gamla gildi� var 5, svo �etta gengur ekki. Hr�ga 3: 0010^0011=0001, n�ja gildi� er 1, en gamla gildi� var 2. �etta er �v� � lagi. Ef vi� t�kum einn stein �t �r hr�gu 3 �� er XOR-�tkoma allra gildanna:

4: 0100
5: 0101
1: 0001
--------
�tk: 0000

Vi� erum �v� � �essari eftirs�knarver�u st��u.

�a� m� rekja sig � gegnum allar hr�gurnar og pr�fa �etta, en �a� er reyndar n�g a� fara beint � eina af �eim hr�gum sem hafa 1-bita � sama s�ti og efsti 1-bitinn er � �tkomunni. H�r a� ofan var 3ja hr�gan s� eina sem haf�i 1-bita � ��ru s�tinu fr� h�gri, sem var efsti bitinn � �tkomunni.

�g vona a� �etta skiljist, amk. af �eim sem hafa eitthva� sp�� essa a�fer�.

[ Next Thread | Previous Thread | Next Message | Previous Message ]