Approaching midnight: what next?
Want some suggestions about where to go next with the game?
Problem
If you are fascinated by being able to win, try playing around with changing the settings of the game (for example, the start time, the time steps, who starts etc.) and see what happens. (You'll need to scroll down the interactive to see the 'Settings' button.)
Can you still find a winning strategy?
Full screen version
Want to see how others played around?
| See what Jennie tried | See what Bernard tried | See what Liz tried |
Let us know your thoughts by emailing us.
Taking it further ...
Student Solutions
Thank you to everybody who had a go at this activity and sent in their thoughts. We received lots of solutions for Approaching Midnight, and these can be found on the solutions page for Approaching Midnight Jump Straight In.
We were sent some solutions specifically for this version of the activity. Riddhi from The Future Foundation School in India said:
1) First to win this game we have to change the settings.
2) Go to the settings and change maximum number of steps or minutes to 60 minutes.
3) Then change the starting time to 11:00.
4) After that, to win you must have the first turn.
5) So, to win just press the 60 minutes button and the time will become 12 midnight.
6) CONGRATULATIONS YOU HAVE WON!
This is certainly one way to make sure you can win the game, Riddhi! Alex from Old Catton C of E School in England also spotted this. I wonder if there are any other changes to the settings you can make so that the first player will definitely win?
Satyaki from The Future Foundation School in India sent in this solution:
I have solved it using 1 minute as the least time limit. You can change the least time limit to 1 minute in the settings. Here you get 60 divisions each varying by 1 minute. It is like having all divisions between 1 minute and 60 minutes.
This is the way in which I got the solution.
Here we will consider the computer's move as a variable which is 'x'. This method only applies if you play first and play with the analogue clock.
This is the method:
Step 1) You move the clock forward to 6:55.
Step 2) Computer's move is 'x', you have to move to 7:56.
Step 3) Computer's move is again 'x', you move to 8:57.
Step 4) Computer's move is again 'x', you move to 9:58.
Step 5) Computer's move is still the variable 'x' but you move to 10:59.
Step 6) Computer again moves 'x' and you can win this time by reaching 12 o' clock.
Remember the first step which is 6:55, because after that each move is 1 hour and 1 minute from where you stopped in your previous move.
Well, this strategy applies for each and every time limit.
You just have to move 1 hour + the least time you have taken to win the game from where you stopped in your first move.
For example, if you take 12 minutes as least time then you will move 1 hour and 12 minutes in the second move from where you stopped in the first move.
So, figure out the first move and then apply the strategy 1 hour + 'n' minutes (where 'n' = the least time limit taken by you in the settings).
This is a really clear general solution, Satyaki - thank you for sharing it with us!
Please email us if you have any other ideas about what to do next with Approaching Midnight that you'd like to share with us.