### Stop or Dare

All you need for this game is a pack of cards. While you play the game, think about strategies that will increase your chances of winning.

### Snail Trails

This is a game for two players. You will need some small-square grid paper, a die and two felt-tip pens or highlighters. Players take turns to roll the die, then move that number of squares in a straight line. Move only vertically (up/down) or horizontally (across), never diagonally. You can cross over the other player's trails. You can trace over the top of the other player's trails. You can cross over a single trail of your own, but can never cross a pair of your trails (side-by-side) or trace over your own trail. To win, you must roll the exact number needed to finish in the target square. You can never pass through the target square. The game ends when a player ends his/her trail in the target square, OR when a player cannot move without breaking any of the rules.

### Game of PIG - Sixes

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

# Can't Find a Coin?

##### Stage: 3 Challenge Level:

Nabeelah from Langley Grammar School commented that:

Your teacher won't know whether you have cheated or not because they can't know what happend because the result can be anything.

Of course this is right but your results could be suspicious if they are very unlikely to occur.

Some people suggested ways in which to get results that appeared likely.

Eloi fromSt. Patrick's Catholic Primary School went about it like this:
We used a coin for the first twenty then we did something similar to it to get our solution.

Phil used this strategy that managed to fool the computer:
I started by making them all heads. I then flipped every second coin. Then I flipped every third coin, then every 5th, 7th, 11th, 13th, 17th ... until I'd gone through all the prime numbers. The computer was sure these were random.

Thomas from High Storrs suggested this:
The best way of making the results seem random is not having equal numbers of heads and tails. If you decide to have more heads then have large groups of heads with a few tails in between in groups of three. If you alter the size of the groups of heads then the results appear random.

Philippa from Ashcroft Academy worked out that Earl had the most suspicious results:
I think Earl is the cheat because his heads and tails are pretty much equal as if he tried too hard to simulate the random pattern of a coin.

Another way of telling that Earl is the most likely cheat is to notice that he has no strings of repeated results of length of 5 or more, and when you realise that there are 95 strings of 6 consecutive results (1st, 2nd, 3rd, 4th, 5th and 6th - 2nd, 3rd, 4th, 5th, 6th and 7th - 3rd, 4th, 5th, 6th, 7th and 8th...) you may find it suspicious that long strings of repeated results do not appear at all.