Bored with the old noughts and crosses? Try this more challenging
4 x 4 version!
The first player puts one cross on the 4 x 4 grid and then the other player enters TWO noughts. The first then enters two crosses and the second two noughts etc.
Any player who gets four in a row wins.
If neither player gets four in a row, then the one who gets the greater number of rows of three is the winner.
For example, in the incomplete game above each player has one group of three so far. You will find it pays to dominate the middle four boxes if possible.
WIN AT NIM!
The word "nim" means "take" in German and in this game players take any number of matches from one of five piles. The last to take a match is the winner. Players take it in turns to set up the piles and no two piles can have the same number. The other player then has the first turn.
You can win this game nearly all the time if you carry out the following calculations:
Break up each pile in your mind into piles which are powers of two, that is 1, 2, 4, 8, 16, 32 etc. Then work out the total number of these smaller piles for each power of two. For example in the piles below I have entered the powers of two in columns:
Total
12 = 8 4
17 = 16 1
10 = 8 2
21 = 16 4 1
15 = 8 4 2 1
In this example there are ODD numbers (3) of 8's, 4's and 1's. The 16's and 2's are balanced with an even number (2) of each. You need to create a balanced situation for ALL the powers of two at each turn. In this example you need to remove 13 (that is, 8+4+1 to balance these powers of two and you will find that you can ALWAYS do this if the game is unbalanced. Take 13 from the last pile in this case. As there are many more unbalanced situations than balanced, your opponent is highly likely to leave it unbalanced on the first or second turn. Once you make it balanced you can continue to do so each turn until you win.
