### Traffic Lights

The game uses a 3x3 square board. 2 players take turns to play, either placing a red on an empty square, or changing a red to orange, or orange to green. The player who forms 3 of 1 colour in a line wins.

### Achi

This game for two players comes from Ghana. However, stones that were marked for this game in the third century AD have been found near Hadrian's Wall in Northern England.

### Yih or Luk Tsut K'i or Three Men's Morris

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and knot arithmetic.

# First Connect Three

##### Stage: 2 and 3 Challenge Level:

In answer to what numbers we should be aiming for, Tom and Chester from Hotwells Primary School said:

It is better to get the numbers in the middle of the board because then you have more choice and it's easer to get three in a row.

Jeremy from Longston School wrote about what numbers are easiest to get:

I wrote a table of all the pairs the dice can throw, and then the numbers you can add and subtract to get

I then made a table of all the totals you can make, and how many ways of making them there are:

 Result How No. ways -5 (1-6) twice 2 -4 (1-5) twice, (2-6)twice 4 -3 (1-4) twice, (2-5) twice (3-6) twice 6 -2 (1-3) twice, (2-4) twice, (3-5) twice, (4-6) twice 8 -1 (1-2) twice, (2-3) twice, (3-4) twice, (4-5) twice, (5-6) twice 10 0 (1-1), (2-2), (3-3), (4-4), (5-5), (6-6) 6 1 (6-5) twice, (5-4) twice, (4-3) twice, (3-2) twice, (2-1) twice 10 2 (6-4) twice, (5-3) twice, (4-2) twice, (3-1) twice, (1+1) 9 3 (6-3) twice, (5-2) twice, (4-1) twice, (1+2) twice 8 4 (6-2) twice, (5-1) twice, (1+3) twice, (2+2) 7 5 (6-1) twice, (1+4) twice, (2+3) twice 6 6 (1+5) twice, (2+4) twice, (3+3) 5 7 (1+6) twice, (2+5) twice, (3+4) twice 6 8 (2+6) twice, (3+5) twice, (4+4) 5 9 (3+6) twice, (4+5) twice 4 10 (4+6) twice, (5+5) 3 11 (5+6) twice 2 12 (6+6) 1

So it is easiest to make $-1$ and $1$.

It is hardest to make $12$ as there is only one way to make it.