As a Y5 class, we worked on the game with a partner using the Chrome books. After a while, I asked children what strategies they used in order to win the game.
One pupil said "We need to reach 10:45 in order to win the game. If you finish at 10:45, it doesn't matter what time you add, as you will be able to reach midnight on your next turn."
A few pupils began to play against the computer. First, they found that it didn't matter if you went first or second as they couldn't win the game. One pupil suggested making a table to record what the computer did. As the computer is programmed to always attempt to reach midnight, they realised they must note down what the computer does and learn from it.
The table below shows one such recording, by Kiran (aged 10).
When playing for a second time, he decided to mimic some of the computer's choices. After some discussions, the class decided that the key times needed to reach in order to successfully reach midnight were:
7:00
8:15
9:30
10:45
After deciding these were the key times, pupils played against the computer and won. They realised that in order to guarantee reaching these times, when playing against the computer, you must go first.
If playing against a person, it may not be necessary to go first, as the opponent might make a mistake (or not know the key times required).
I am submitting this summary of the investigation on behalf of my class. I have included an example of Kiran (one of the pupils) as this shows his working methods and realisations.
I also challenged a small group to work out a way of winning against the computer when the time started at 5:30 and you could choose times ranging from 15-120 minute intervals. On whiteboards, using a similar method to the first, they played and worked out how to win against the computer by going first. Max and Kiran noticed that the computer had two distinct patterns it followed when 120 minutes were selected first.