It's play time, Children.

In this blog post I thought I'd provide some answers to, and in part ruin a few time wasting class games; 21 and noughts and crosses.

 Counting - 21

21 is a counting game, for those who don't know, in which players take it is turn to say between 1 and 3 consecutive numbers up until 21, the person who says 21 looses. For example: 1 2, 3 4 5, 6, 7 8, 9 10 11, 12, 13 14 15, 16 17 18, 19 20, 21 and red wins.

A lot of people have already debunked this game, but for those who haven't, it can be rather embarrassing. The idea behind this game revolves around multiples; in 21 the key number is 4. 21 is not a multiple of four, but 20, is:

1111
1111
1111
   1

With this you can see that once all the multiples of four have been said the next person has lost. It is your job therefore to say the last multiple of 4.

 Multiples of 4 in this case are the way to go. If you as the player say 4 then you have won, so long as you keep on your toes. You can keep saying the next multiple of four as long as you have said the previous one as the difference is never achievable in the opponent's one go ie. 1, 2 3 4, 5 6, 7 8, 9 10 11, 12, 13 14, 15 16, 17 18 19, 20, 21 Orange wins as he always keeps onto the multiples of four. This principle works for all 'counting to' numbers one after a multiple of four, 13, 401, 50197 etc...

The same idea can be applied to other games if you want to change the numbers around - a fair few people have cracked 21 and by changing it up may throw them off. Take 34 as the number to count to; one greater than 33, a multiple of 3. You can count up in numbers of 2. ie. 1 2, 3 4, 5, 6 etc. in each case the person who says the first multiple of 3 can keep onto consecutive multiples of 3 for the rest of the game and win it with the same principle as above.

So if you want to compose a game where you can say up to 5 numbers, and win, then take a multiple of the number 6 (one above the counting number) and then add one ie. 37 (the number to count to) and go second, keeping to the multiples of 6. Try to steal these multiples from an opponent if they don't know the value.

Say to them; "I'll go first to show you how it's done". When you presumably win they will assume it had something to do with going first even though second is actually the better position, setting you up for later games when they ask to go first.


Noughts and crosses

There are a set of moves to learn that means you can never loose a game.

    1    ¦  2    ¦  3            
___ __¦__ __¦____            
    4    ¦  5    ¦    6  
___ __¦__ __¦____
    7    ¦   8   ¦   9   
          ¦        ¦

Drew up this labelled square so it's easier to refer to individual squares. 'X' are used for our move; 'O' for the opponent.
The whole game is much easier to win when you start first, there are two opening moves to go with that will help lead to a win, either the middle square (5) or one of the corners (1, 3, 7, 9, ) which all behave the same. 

If you start in the middle (5) then they have the option to go either on a side or a corner. 

If they go in the side, say 2, then you should go 3 (or 9). This sets up a position where they have to block you at 7 to stop a win there. After you can set up this 'V' on its side shape (3, 5, 9) whereby there are now two options for winning, at 1 or 6, the opponent can't defend against the both and so looses.

          ¦   O  ¦   X            
___ __¦___ _¦____
          ¦  X   ¦
___ __¦_ ___¦____
   O    ¦        ¦   X
          ¦        ¦         

You've started in the middle and now the opponent goes for a corner space, say 1. By going now for 9 on the opposite side you start to set up this sideways 'V' again. At this point he can either choose for an edge, where he looses or a corner where he draws.
 If he chooses the edge at 2, go for 3; the sideways V and win on 6 or 7. If he goes for 6, go for 7 setting up this upside-down 'V'. This V is the key. Top pic. below.
If after 5, 1, 9 he goes for either corner piece then he will stop this V forming and stop you winning - a tie. Second pic. below.



     O  ¦        ¦                
___ __¦____¦____
    O   ¦  X   ¦   
___ __¦_ ___¦____
     X   ¦        ¦   X  
          ¦        ¦        


     O  ¦        ¦                
___ __¦_ ___¦____
          ¦  X   ¦   
___ __¦_ ___¦____
     O  ¦        ¦   X  
          ¦        ¦        


Instead by going in a corner, as the opening move, use a three corner square to set up the "can't defend against two at once". 
Start with a corner, say 1. There are many possible moves he can run from here; middle, opposite corner, non-opposite corner, attaching side or non-attaching side. Each has a different outcome.
1) If he chooses the opposite corner ie, 9 to your 1; then go for another corner, he blocks you and you set up the same 'three corner plot' to win
2)If he chooses the non opposite corner then exactly the same principle applies, choose the opposite corner first to make him block you then 'three corner' him to win. 
3)If he chooses conjoining side ie, 4 to your 1 then choose the corner remaining that is not opposite ie; 3 this sets up the same as before to win
4)If he chooses non-conjoining side ie, 6 to your 1 then choose a non-opposite corner and the same principle to win.
5) If he chooses the centre then form a straight line diagonal at 9. A corner move from him will allow you to set up this three corner set and win on one of the sides. ie: 1, 5, 9, 3, 7 then win on 4 or 8.
6) In fact the only way that the opponent can draw to this strategy is by going to the centre, you going opposite and then him going on a side ie; 1, 5, 9, 2, he forces you to block him at 8 and so you don't get to set up your three corner.


5)  X   ¦        ¦   O            
____ _¦___ _¦____
          ¦   O  ¦   
__ ___¦_ ___¦____
     X   ¦        ¦   X  
          ¦        ¦        


When you go second, then you can only force a draw unless your opponent slips up. You can do this by stopping the two patterns ((the V shape ie; 1, 5, 3 when they start with the middle) or (the three corners ie; 1, 3, 7 when they start in a corner))
Play between decent players will always end in a draw, as there are just so few possible variations to the game.

Was a long one today
:)

Until next time xx