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  4. Approaching Midnight

Approaching Midnight

Full Moon
 

Can you beat the clock to the midnight hour?

Move the clock forwards by clicking the buttons. If you're the first to get to midnight, you win!

Play the game against the computer as many times as you like.

Can you find a winning strategy? If so, post a comment below and describe what you did!

 

See here for some hints to get you started.

See here for some ways of taking the game further.

See here for the ultimate Approaching Midnight challenge!

If you'd like to play similar games, have a go at Got It and Seven Counters. Can you see how they are linked?  (You may like to read our Playing the Same Game article.)

Share your thoughts and discoveries

Comments

Submitted by Joe on Fri, 01/15/2016 - 16:13

The way to win is to get the computer to 11:45

Submitted by Torin on Tue, 03/08/2016 - 13:15

actually 10:45

Submitted by emp1001 on Tue, 03/08/2016 - 13:27

Hi Torin,

Thanks for your comment. Can you give us a bit more detail? Are you suggesting that you need to get the clock to 10:45 in order to win? How do you know?

Submitted by JEFF on Tue, 06/21/2016 - 11:07

you do need to get 10.45, but also 9.30

Submitted by The Person on Mon, 06/27/2016 - 10:02

First do 15 mins

Submitted by Anonymous on Wed, 09/14/2016 - 23:30

You have to not let the computer lock you in at 9:30. You also have to not let the computer to 10:45

Submitted by emp1001 on Tue, 01/19/2016 - 11:53

Thanks for your comment, Joe. Do you mean that you want to have your turn when the computer has made the time up to 11.45? I can see that would mean you would choose 15 minutes and you would win.

How will you make sure that this happens?

Submitted by Mariah on Sat, 01/23/2016 - 06:28

The way to win 'Approaching Midnight' is to make the computers final turn at 10:45, so no matter what they press (15, 30, 45 or 60 minutes) you will be able to reach midnight first. This is because 10:45 is 1 hour and 15 minutes before 12:00. 1 hour and 15 minutes is the only possible time that can be reached round of your turn and the computers, as 1 hours and 15 minutes equals 75 minutes. If the computer choses 60 minutes then you will chose 15 to equal 75, the same goes for 45 and 30, 30 and 45, 15 and 60.

The way to make sure the computers final turn starts at 10:45 is using the same 75 minute pattern.

Starting first, you press 60 minutes, from then on, (so starting at the computers first turn) every round must equal 75 minutes (60 minutes + 75minutes x 4 = 360 minutes or 6 hours, the needed time)
Your next move, and every move after will depend on the computer. If the computer moves the clock forward 60 minutes, you move 15, in the same way you would on the final turn, as explained above.
Alternatively you can just wing it and hope your very, VERY lucky.

Submitted by emp1001 on Sun, 01/24/2016 - 20:41

Thank you, Mariah, for sharing your way to win. I have hidden the final bit under a 'reveal' button so that others can choose to look at your strategy if they want to, rather than it being a 'spoiler'!

Have you tried changing the settings of the game? For example, how would your strategy change if you altered the start time? Take a look at Approaching Midnight: What Next? for some suggestions.

Submitted by Aila on Sun, 02/14/2016 - 20:52

This is a really fun game to play because it involves using your logic! I need to find a solution that will work for me because the 1hr and 15 min doesn't work!!

Submitted by emp1001 on Tue, 02/16/2016 - 14:36

Thanks for your comment, Aila. Could you describe what you have tried?

Submitted by Amy on Tue, 03/15/2016 - 19:38

On the digital clock it helps if you try and get to 15:15. Also, you automatically win if you get 22:45.
Hope this Helps!

Submitted by emp1001 on Wed, 03/16/2016 - 16:27

Thank you for your comments Amy. How do you know that these times are important? Can you tell us a bit about your thinking?

Submitted by Jazmin and Heather on Mon, 03/21/2016 - 14:26

Independantly, we tried to figure out the strategy behind this game. Eventually we both came up with a winning formula which has proved to work each time you play. The formula we found that worked best for us was:

For the 6 hour version of this game you need to reach some allocated times in order to win.You have to work in the multiples of 5 and each block of 15 minutes corresponds as 1/5 this means that if the computer moves 3 blocks then you have to move 2 blocksof 15 minutes to make it equal 5.

7:00
8:15
9:30
10:45
12:00

For the 18 hour version of this game you need to reach some allocated times in order to win:

You have to work in the multiples of 5 and each block of 15 minutes corresponds as 1/5 this means that if the computer moves 3 blocks then you have to move 2 blocksof 15 minutes to make it equal 5.

6:30
7:45
9:00
10:15
11:30
12:45
14:00
15:15
16:30
17:45
19:00
20:15
21:30
22:45
24:00

Submitted by emp1001 on Tue, 03/22/2016 - 10:43

Thank you for your well explained post, Jazmin and Heather. I have hidden most of it under a 'reveal' button so that we don't give away too much, in case others would like to try the game for themselves first!

Do you think you could explain how to win this game if you had any start time?

For another challenge, have you tried playing with different blocks of time?

Submitted by noobslayer564 on Tue, 07/05/2016 - 08:32

Thanks, Jazmin and Heather, that is very helpful but what if you start at 4 o'clock?

Submitted by Nathan on Fri, 03/25/2016 - 11:11

It is essential that you make sure that you start with your first move being one hour. There are several times that you are looking to get to:

8:15,9:30,10:45 and obviously midnight.

The best way to do this is to think carefully about your next moves and the possible moves that the computer could make.

Submitted by emp1001 on Tue, 03/29/2016 - 08:44

Thanks Nathan! I've hidden some of your advice under a 'reveal' button so that others have chance to think about what the times might be. How did you work out this strategy?

How would your strategy change if the start time on the clock was different? For example, what would you do if the start time was 5 o'clock?

Submitted by Donald Lowery on Wed, 05/18/2016 - 00:25

This game is the same as the "Got It" game elsewhere on this site. Here is the solution for any settings chosen:

Every move you make the following equation true:

ChosenTime modulo (#ofChoices+1)*(SmallestStepAllowed) = (720-StartTimeInMinutes) modulo (#ofChoices+1)*(SmallestStepAllowed)

Where the #ofChoices is equal to the BiggestStepAllowed divided by the SmallestStepAllowed.

This formula becomes simpler when the minutes are converted to steps:

ChosenStep modulo (#ofChoices+1) = #ofSteps modulo (#ofChoices+1)

Submitted by emp1001 on Wed, 05/18/2016 - 08:10

Thanks for your comment, Donald. I have hidden most of it under a 'reveal' button so that other people can choose whether or not to read it.

I wonder whether any of the other games in this pathway equivalent to Got It.

Submitted by Anonymous on Mon, 06/27/2016 - 10:08

You need to get certain times in this order:

7:00
8:15
9:30
10:45
And of course MIDNIGHT

Submitted by 5R maths club on Mon, 06/27/2016 - 11:59

You need to start.
There is 4 check points.
Two of them are 7:00 & 9:30.

Good luck at finding the other two and at winning this strategic game.

Submitted by Dame Bradbury's... on Tue, 07/05/2016 - 08:26

First get to ...

7 pm then 8:15, then 9:30 then 10:45

and then you can win!

Austyn, George, Oliver S and Sukie

Submitted by Nathan Burn on Fri, 07/29/2016 - 17:18

To win you must start: Make 7:00 to start with, and then make subsequent times of 8:15, 9:30, 10:45 and finally 12:00.

Submitted by Nathan666 on Sun, 09/04/2016 - 11:01

If you read my earlier submission, then you know what to do at 6 o'clock, but if you are to win at 5 o'clock, you must start.

From 5 o'clock, you must choose 45 minutes, so that there is an hour and 15 min gap between 5:45 and 7:00. This means that whatever time the computer chooses, you can make 7:00, and then subsequent times of 8:15, 9:30, 10:45 and finally 12:00.

Submitted by Nathan666 on Sun, 09/04/2016 - 11:11

From 4 o'clock ...

You have to try to give the computer 7:00 eventually. Therefore, make 4:30, 5:45, and then 7:00, and following the steps from my 6 o'clock solution, complete with the following times: 8:15, 9:30, 10:45 and midnight.

Submitted by Nathan666 on Sun, 09/04/2016 - 11:12

From 3 o'clock ...

You have to try to give the computer 7:00 eventually. Therefore, make 3:15, 4:30, 5:45, and then 7:00, and following the steps from my 6 o'clock solution, complete with the following times: 8:15, 9:30, 10:45 and midnight.

Submitted by Nathan666 on Sun, 09/04/2016 - 11:15

From 2 o'clock ...

You have to try to give the computer 7:00 eventually. Therefore, make 3:15, 4:30, 5:45, and then 7:00, and following the steps from my 6 o'clock solution, complete with the following times: 8:15, 9:30, 10:45 and midnight. However, since it is impossible to immediately make 3:15 from 2:00, then you must make the computer start and then make the above times.

Submitted by Nathan666 on Sun, 09/04/2016 - 11:17

From 1 o'clock ...

You have to try to give the computer 7:00 eventually. Therefore, make 2:00, 3:15, 4:30, 5:45, and then 7:00, and following the steps from my 6 o'clock solution, complete with the following times: 8:15, 9:30, 10:45 and midnight.

Submitted by Nathan666 on Sun, 09/04/2016 - 11:19

From 12 o'clock (NOT midnight) ...

You have to try to give the computer 7:00 eventually. Therefore, make 12:45, 2:00, 3:15, 4:30, 5:45, and then 7:00, and following the steps from my 6 o'clock solution, complete with the following times: 8:15, 9:30, 10:45 and midnight.

Submitted by Nathan666 on Sun, 09/04/2016 - 11:29

starting from the 6 o'clock in the morning ...

you must make: 6:30, 7:45, 9:00, 10:15, 11:30, 12:45, 14:00, 15:15, 16:30, 17:45, 19:00, 20:15, 21:30, 22:45, 00:00

Submitted by emp1001 on Tue, 09/06/2016 - 12:21

Thank you for your detailed comments, Nathan. I have hidden some of your posts under 'reveal' buttons, just so that other users have to choose to see your strategy.

I wonder whether you can explain a general way of winning - for any start time - if the times to choose are 15 mins, 30 mins, 45 mins and 1 hour.

Have you tried changing the settings to choose different time intervals? How does that affect the game?

Submitted by Rob D on Sat, 09/10/2016 - 09:42

Every round needs to equal 75 minutes.
This is because ...

to win you need to get to 10.45, this is 1 hour 15 minutes before midnight.
In order to get to 10.45 you need to go back 75 minutes to 9.30.
From there you can just carry on playing so both your own and the computers turns are equal to 75 minutes
So if the computer played 15mins you would play 60 mins.
12
10.45
9.30
8.15
7 - Key Number
To start the round you have to play 60mins in order to take it to the computer's turn then you just play the method above.
eg.
6.00
You MUST 60mins
7.00
PC plays 45 mins
7.45
You MUST play 45mins
8.15
PC plays 15mins
8.30
You MUST play 60mins
9.30
PC plays 30mins
10.15
You MUST play 30mins
10.45
PC plays 60mins
11.45
You MUST play 15mins

Submitted by emp1001 on Mon, 09/12/2016 - 13:20

Thanks for your comment, Rob. You'll see I've hidden most of it under a 'Reveal' button so that other people have to choose to read it, rather than us giving the game away immediately.

Have you tried changing the settings of the game?

Submitted by lilyrose on Sat, 11/12/2016 - 10:45

kind of hard not much. got it once out of 31 goes don't let the computer go on 8: 3o 9:3o and 10:45
well good luck !!!! I'm on your side if it is hard.
ps. go hard rock

Submitted by Rebecca on Tue, 11/22/2016 - 22:46

You can always win if you're the first player when it starts a six o'clock because of the times that you can move ...

Essentially, you want your opponent to move at 10:45- the least they can do is 11 o'clock, at which point you move an hour, and the most they can do is 11:45, at which point you move 15 minutes. In order to ensure that they move at 10:45, you must ensure they move at 9:30- one hour and 15 minutes prior to 10:45. In order to make sure they move at 9:30, they must move at 8:15, again, one hour and 15 minutes prior to 9:30. Similarly, in order to ensure that they move at 8:15, they must move a 7 o'clock. As it starts at 6 o'clock, you move an hour to begin with. As long as you make sure that they hit each of those times in turn, you will win. If you aren't playing first and the computer goes first, then you are guaranteed to loose if they follow this strategy.

Submitted by emp1001 on Wed, 11/23/2016 - 15:54

Thanks for your comments, Rebecca. I have hidden most of them under a 'reveal' button so that we don't give the game away for others straight away.

Have you tried changing the settings on the game? How would you win if the start time was seven o'clock, for example?

Submitted by Riya on Thu, 01/12/2017 - 12:39

To win you have to go to...

7:00, 8:15, 9:30 and then to 10:45


This strategy will make you win 100%

Submitted by emp1001 on Thu, 01/12/2017 - 14:14

Hi Riya,

Thanks for your comment. I have hidden most of it under a 'reveal' button so we don't give the game away too easily!

How might you play differently if you changed the start time?

Submitted by Maeve on Sat, 03/11/2017 - 19:40

Basically, 60=4, 45=3, 30=2, 15=1. You need to

get to 3, then 8, then 13, then 18. This is because all of these put the computer in awkward situations when however much the computer adds, [4, 3, 2, 1] you have the upper hand. 18 is the most crucial one.

PS This strategy also works for Got It.

Submitted by matthew on Thu, 04/27/2017 - 11:12

The idea of treating your moves as steps of 1, 2, 3 or 4 sounds very promising. However, while your strategy works for Got It, it doesn't quite work for this problem. They are very similar problems, but this one is aiming to get to 24, rather than 23. So how does this affect the numbers you need to reach?

Submitted by Aman Bansal on Thu, 05/18/2017 - 14:06

The trick is to try and give the computer the move at times 12:00 - 1:15 hours.

This means that it should be the computer's turn to move at 7:00, 8:15, 9:30 and 10:45, otherwise you lose the game and have to retry.

Submitted by matthew on Thu, 05/18/2017 - 14:13

That's an excellent strategy. I have hidden it under a 'Reveal' button so that others can have a go without seeing your solution if they want.

How would your strategy change if the allowed steps were different? What if the start time was different?

Submitted by Aman Bansal on Sun, 05/21/2017 - 14:49

Let's say the ending point is y and the number of combined moves we AND the computer make is x (our turn followed by the computer's is counted as only 1). Also the biggest move one can execute is h and the smallest move is s.

Then, my strategy is to try and get our opponent's turn at all of the y-x(h+s) positions. In other words, each combined move must be equal to h+s. So we use our turn to reach those positions.

In the example of approaching midnight, y = 12:00, h=1:00 and s=0:15.
Therefore to win this game, we must try and get our turn at all of the y-x(h+s) positions which is all of the 12:00 - x(1:00 + 0:15) positions.

Also, the start time does not matter as it doesn't intervene in the expression y-x(h+s). Only things that matter are the end time, the biggest step one can make, and the smallest step one can make. Unless the start time is at a y-x(h+s) position, in which case the game becomes unwinnable (unless our opponent goes first).