What is the total number of strategies (pure strategies in game theory) in a Tic Tac Toe game for each player? Assume that  it is a 3x3 game and 2 players.   Rule: The players put marks such as X and O sequentially. Both players observe all choices. The first player to have 3 of his/her marks in a row (horizontally, vertically or diagonally) wins.   I was looking at this post () but it is a specific case that only considers winning strategies.   My solution strategy:  I know that there are 9! ways to play this game for one player, which is 362880. BUT this is the case if the game does not end in 5th, 6th or other moves. I am not really sure how to add in these factors.
How many combinations are possible in the game tic-tac-toe (Noughts and crosses)?  So for example a game which looked like: (with positions 1-9)  A1   --   B1  A2   --   B2  A3   --   --   [1][3][4][6][7] would be one combination
Is losing privileges after placing bounty OK? My rep went over 2,000 today which meant I could edit other people's posts. Great! Then I added a bounty to a previous question, which brought me back down to 1,984...and I can no longer edit other posts. Should this changed? Or is this ideal? How do I install transition molding between my new hardwood and existing tile floors? I have ripped out some old carpet and am preparing to install a new solid hardwood floor myself.  In several places, the floor transitions to an existing tile floor.  The hardwood floor guys told me the best transition between the two is a T molding.  You simply leave a gap between the two floors, and then place down the T molding between the two floors, so it sits on both surfaces.  Sounds simple enough.  However, the height difference of the two floors is considerable, and the T molding does not sit flush.  What are my options?  Here is a diagram showing the dimensions.      NOTE:  Using the T molding is not a requirement, I could go some other route if there is a better option. I have been playing around with Ubuntu installing new themes and and docks. Sometimes during the installation, whole screen just hangs. What is the best way in Ubuntu to Kill a process/application? Anything similar to Ctrl + Alt + Del of windows? Find the exact value of the infinite sum $\sum_{n=1}^\infty \big\{\mathrm{e}-\big(1+\frac1n\big)^{n}\big\}$ How can we find the exact value of the infinite sum  $$ \displaystyle\sum_{n=1}^\infty \left\{\mathrm{e}-\Big(1+\frac1n\Big)^n\right\}? $$  This problem appears in:  , p.114. ...And you jumped in.  What would happen when you got to the middle of the Earth? Would you gradually slow down, until you got to the middle and once you were in middle would every direction feel like it was up? I am having Problems converting user rights. I want to assign the following rights to certain files/folders but dont know hat to translate them into a format which chmod will work with like chmod 755.  -rwxrwxrwx    will be?  And  drwxr-xr-x   will be?  And finally  -rw-r--r--   will be? Theoretical Proof of Pauli's Exclusion Principle Count number of occurences for each unique value Slave duplicate counter Is it possible to create a counter that is a "slave" to another (master) counter, but also an exact duplicate?  The \@addtoreset{&lt;slave&gt;}{&lt;master&gt;} resets &lt;slave&gt; whenever &lt;master&gt; is incremented (similar functionality is offered by ), but I don't know about anything incrementing one counter (&lt;slave&gt;) automatically whenever another counter (&lt;master&gt;) is incremented.  The idea is to have a macro (say) \dupcntr{&lt;slave&gt;}{&lt;master&gt;} as an analogue to \@addtoreset. The application for this might be where one is interested in renaming a counter used/provided by a package into something more meaningful for the user (say, &lt;slave&gt;), without having to reference &lt;master&gt;. Or, if the original counter contains @ that needs to be escaped every time it's used, it is sometimes more convenient to have a "more user friendly" counter.  I know one way around is to use a macro that returns the value of &lt;master&gt;, but is it possible to perform the same manipulation with a macro than one could with the counter? Manipulation here refers to the printing of the counter (via \the&lt;slave&gt;) and perhaps it's representation (like \arabic, \alph, ...). Details on how the Yearling badge works Jawa asked me this  and I didn't know the answer. So I present it to the meta SO community:     [To get the Yearling badge] Do you need to earn the 200 rep within that one year or is it enough to get 200 at some point after being a member for a year? And does 'a year' mean the very first 12 months or the last (sliding window of) 12 months?    I would assume that if you hit 200 reputation after you've already been around for a year, then you would get the Yearling badge. But I don't know. What are the key principles that effective designs share? You have arrived on this page because you are clearly curious about underlying fundamentals that you can incorporate into your thought process when designing.  According to many that came before us, there are key principles that can be considered when creating an effective design. In the following answers, you will find useful theories from a variety of respected sources.  Use this question as a reference for navigating the variety of topics:  Gestalt Principles  &nbsp;&nbsp;  &nbsp;&nbsp;  &nbsp;&nbsp;  &nbsp;&nbsp;  Other Fundamentals and Useful Information  &nbsp;&nbsp;  &nbsp;&nbsp;  &nbsp;&nbsp;  &nbsp;&nbsp;  If you know of a topic that hasn't been covered here, please add an answer with references to respected resources and it will be added to the list.  Of course direct quotes and paraphrasing from respected resources are a must, but should be limited to a small paragraph per topic at most and referenced back to their source as thoroughly as possible.  A  has been posted before, but not to create a collection of snippets that are enlightening for graphic designers of any and all skill levels. Merging bib files from within LaTeX The topic which haunted me for two years until I gave up on it. But now I am doing engineering and this topic suddenly popped out of my textbook from nowhere. I seriously need to understand this topic because I wasn't able to do so in the past. I have read many book on 'energy' and it came to nothing. Maybe just because the many books I have read all said 'energy' is something which doesn't 'exist'! It is 'abstract'! It is just a number which represents the state or orientation of a system. But then I see so many examples that 'uses' energy to do 'work'. But the question here is that if anything doesn't exist in this universe, then how can the same thing be used to do something that exist?  My problem is that I didn't understood the topic 'energy' and all the other topics related to it (work, power etc.) NOR Gate is Working Correctly with Vcc Pin Disconnected anyone tell how is this effect created which change lips color to orange and little orange on face without brush etc tool how to change the only lips color to orange without brush etc tool and how this is created and little orange on face Can the off-regional pokémon hatch from eggs? Some people claim you can get the pokémon that are not in your region from eggs. Is this only a rumour or actually true? I've seen off-regional pokémon in gyms nearby but I can't rule out that the owner had been abroad or maybe even used location spoofing. Export multiple objects to .obj It is possible to export all object from a scene into different obj files (each object in a obj file separately)? Site specific magic comment links System freezes completely with Intel Bay Trail My system freezes completely at random, frequent intervals. I started to have the same problem in Ubuntu 14.04 but after recent upgrade to 16.04 there is no improvement, in fact it seems worse.  When it happens, it's impossible to do anything. I've tried everything in this thread:  but nothing works, I have to hard reset. I have read all the system logs and journalctl but there is never any information that could help diagnose the problem.  This is a dual-boot system with Windows 10 and there's no problem there, so it's not defective hardware.  My laptop has an Intel Bay Trail processor (Pentium N3540) Finite ring has only zero divisors and units If a nonzero element $a$ of a ring $\mathbb{D}$ does not have a multiplicative inverse, then $a$ must be a zero divisor.   If $\mathbb{D}$ has finitely many elements, then the statement is true. However, I don't see why, as for the infinite case, 7 isn't a zero divisor only because every element $a &gt; 0$ when multiplied by a $b &gt; 0$ gives you $ab &gt; 0$ which has nothing to do with infinity or finite amounts of elements.