1. Pathways
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  3. Got It!
  4. Got It

Got It

 

Can you be the first to get to 23?

Got It is a game for two players. The first player chooses a whole number from 1 to 4. After that players take turns to add a whole number from 1 to 4 to the running total. The player who hits the target of 23 wins the game.

Have a go at playing the game as many times as you like. You could use the interactive below.

 

Tablet/Full Screen Version

 

 

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

If you have mastered the game, then see how to take it further.

To play similar games, see Approaching Midnight and Seven Counters. Can you see the similarities?  (You may like to read our Playing the Same Game article.)

 

Comments

Submitted by Raymond on Tue, 12/01/2015 - 23:33

I have played a variation of this before. The version I have played is basically the same thing, except up to 21 and you are allowed to use the numbers from 1-5.

The trick to winning is game is to be the first player. If you start with 3, you shall always win...if you know what to do afterwards.

First, start with 3. This solution uses the fact that no matter what number your opponent says, you can always add them to make...5, correct. For example, if your opponent selects 1, you can choose 4. If they choose 2, you can choose 3 and so on. Since it always makes 5, 23 divided by 5 makes 4 remainder 3. So start with 3 and you shall win.

If you don't understand this, just try playing the game. Ensure that you are starting first and say 3. Whatever the next number they say, make sure that their number and your next number adds to 5. For example, if they choose 3 as well, say 2. If they say 4, say 1, and so on. Eventually, it will be YOU who's the one that says 23...

If you follow these rules, it is certain that the game will be good...for you only I mean.

Submitted by dp419 on Thu, 12/03/2015 - 10:18

This is a really good explanation - well done! I've hidden the explanation (just click the reveal button), so that it doesn't spoil the solution for everyone else who don't want to see it.

Submitted by Roxy on Tue, 01/31/2017 - 17:31

I tried you strategy and it's really hard I really don't get it.What do you do after putting 3.

Submitted by Ole on Thu, 12/10/2015 - 00:34

Make sure that the other player always must add to a number that is a whole number of times the lowest number plus the highest number lower than the end number.

Submitted by emp1001 on Thu, 12/10/2015 - 09:37

Thank you for posting. I wonder whether you could help me understand what you mean by 'the highest number lower than the end number' please. Perhaps going through an example would help?

Submitted by Bubblegum on Tue, 04/05/2016 - 15:22

If YOU have the number 18 no matter what you will win

Submitted by mf344 on Fri, 06/17/2016 - 11:42

Good thinking, Bubblegum! Can you figure out to make sure you end up with an 18?

Submitted by EpicNinja on Wed, 07/06/2016 - 16:29

Get 8 and 13

Submitted by BlueGirl on Thu, 10/20/2016 - 03:33

You need to get 3 too.

Submitted by Andrea on Sat, 02/18/2017 - 09:52

Yes, you need 3,8,13,18 and if you start with 3 you will get them all.

Submitted by emp1001 on Tue, 04/05/2016 - 15:35

I agree, 18 seems like an excellent number to make the total up to. Can you explain why this will mean you will always win the game, no matter which number the other player chooses?

How could you make sure you always get to 18?

Submitted by Laura on Wed, 08/17/2016 - 06:47

you must start with ...

3, then get to 8, then 13, then 18 and you will win.

Submitted by crimzonghoul on Wed, 11/30/2016 - 20:39

Your theory is flawless with the settings 23 total and 1-4 as options! ;D

Submitted by Fabio Milner on Fri, 04/08/2016 - 22:01
Note that each player must add at least one and at most 4. If you want to be in control of the game (and win it), then you must ...
... skip back by fives (1+4) from the winning number down to the first positive number that you are allowed to choose: 23, 18, 13, 8, 3. Hence, if the first player picks the number 3, (s)he is certain to be able to pick 8 as second number (no matter what the other player chooses), 13 as third number, 18 as fourth and 23 as the 5th number.

Submitted by emp1001 on Tue, 04/12/2016 - 08:43

Thank you Fabio for clearly setting out how you can win this game. As with some of the other comments, I have hidden part of yours under a 'reveal' button so that other people can choose whether or not they look at your suggestions.

What would happen if the goal is 25 rather than 23?

Submitted by Sid on Sun, 06/05/2016 - 04:17

Set the computer to go first. Make sure at the end of every second turn, the total is a multiple of five. Continue for your win.

Submitted by Vibhav sugumar on Wed, 04/20/2016 - 10:59
If you play 3 the computer has no choice....
... because you need to get 8 then 13 then 18. It doesn't matter what the computer does. Say it does 3, so the total is 6 you need to get to 8, so play 2. The total is 8 and it's the computer's turn, say it plays 1, then the total is 9, you play 4 the total now is 13. Say the computer plays 4, the total is 17, you play 1 to get to 18. The computer plays 2 the total is 20 and then you play 3 and you win.

Submitted by mf344 on Fri, 06/17/2016 - 11:45

Thanks Vibhav, that's exactly right. I have hidden your answer behind the reveal button, so we don't spoil other people's fun figuring it out. But is 3 the only starting move that will get you to win?

Submitted by Vibhav sugumar on Wed, 04/20/2016 - 11:00

There is a solution to win whatever the number is.

All you have to do is add the smallest number to the biggest number option and keep taking away that number from target until the smallest number is reached. The way to win is to keep hopping through all the different target numbers you have worked out by take away. So if the target to get is 29 and the numbers are 1-6 keep taking away 7 from 29 the numbers which you land on are the targets.

Submitted by mf344 on Fri, 06/17/2016 - 11:48

Again, great thinking Vibhav, well done! Can you explain why that works?

Submitted by wild maths club... on Wed, 04/20/2016 - 11:53

When the target is 21 and you can only choose 1 2 or 3. You go up 1 then 3 every time and you will always win. This will only work against the computer and you go first!

Submitted by mf344 on Fri, 06/17/2016 - 11:49

Hi wild maths club! That's a great approach! Can you explain it further?

Submitted by Lucs on Wed, 04/20/2016 - 13:45

The winning strategy is:

3,4,4,4,4

Submitted by Oscar J on Wed, 05/11/2016 - 14:10

Thanks a lot, Lucs, that really helps me figure out a formula that made sense.

Submitted by mf344 on Fri, 06/17/2016 - 11:49

Hi Lucs! Sounds like you are on to something. Can you explain it further?

Submitted by gmp26 on Thu, 04/21/2016 - 16:49

Now can you beat it? Is there a more general rule?

Submitted by Dyan, Bethany, Leia on Fri, 04/22/2016 - 08:22
If you get to 8 then 13 then 18 you will win.

Submitted by gmp26 on Fri, 04/22/2016 - 08:52

I have a few questions.
1. How would you stop the computer getting to 8 first?

You can change the settings and get a different game
2. What would you do if the target were 24, or 25, or 26, or 34?
3. Staying with a target of 23, what would you do if you could add up to 2? or 3? or 5? or 6?

Submitted by Unknown on Wed, 05/04/2016 - 20:24

I know the winning method!

First, you need to get 8. Then 13, then 18 and then you win by getting 23! here's an example: If I choose 3, and com does 2, and I choose 3, and com chooses 4, and I choose 1, and com chooses 4, and I choose 1, and come chooses 4, and I choose 1 I'll get 23. Try this method, but I don't guarantee the computer repeating the sequence so, if something changes, as long as you get these numbers you win!!!

(if my explanation is similar to anyone else's, sorry, but I did not check anyone's explanation as i like to do things myself)

Submitted by mf344 on Fri, 06/17/2016 - 11:53

Hi there. You're totally right, much better to figure it out for yourself! And your idea is great! Can you explain why it works?

Submitted by sam sloan on Wed, 05/11/2016 - 14:05

You have to add the smallest...

..and largest of the possible numbers you can add on (lets call this 'x'). If the target is a multiple of 'x' then you let the computer go first and whatever he chooses you have to choose to number that adds to 'x' (with the number that he chose. However if the number is not a multiple of 'x' then you go first and make it the next multiple of 'x' by subtracting a number, then you carry on the strategy before.

Submitted by GRAHAM on Thu, 05/12/2016 - 08:38

Thanks found this really helpful

Submitted by mf344 on Fri, 06/17/2016 - 11:57

Well done Sam!! Can you explain why this works?

Submitted by Oscar J on Wed, 05/11/2016 - 14:09

If you set the computer to go first, and the target number is 21, once the computer reaches 15, you lose. If YOU find a way to get to 15, you win almost no matter what happens next, (If you know how to play...)
If you have something to tell me, please respond.

Submitted by mf344 on Fri, 06/17/2016 - 11:57

Hi Oscar! That sounds like you're on to something! Can you explain it further?

Submitted by Rui Xiao on Thu, 05/26/2016 - 18:44

We broke the code :) .

If the target is 23 and the adding total number is 4, then you should use the target number 23 subtract 5, which is the total number 4 plus 1, then you continue subtract till the lowest number, you will get numbers like 18, 13, 8, 3, use these numbers when you add, starts with 3, then you will win.

This rule can be used for other target numbers, please try. Good luck!

Submitted by mf344 on Fri, 06/17/2016 - 12:00

Hey Rui, very good thinking!! I've hidden your answer so that other people can figure it out for themselves.

Submitted by vaishanav on Fri, 05/27/2016 - 16:31

To win the game...

.. it's the max you can choose plus one divided by the target and the remainders times tables are the "safe numbers" so no matter what the computer chooses you will win try and see if I am lying or not.

Submitted by mf344 on Fri, 06/17/2016 - 12:02

Hi Vaishanav,

Sound alike you're definitely on the right track. Can you explain this further? What do you mean by "safe numbers"?

Submitted by Mohamed Ismail on Thu, 06/02/2016 - 18:02

Let's say...

max is the maximum number you can add, there is a winning path of numbers to go through in order to win in any case, you should begin with (target modulo max +1) and reach +5 at each step. target= 23, max =4, you should begin with (23 % (4+1)) wich is 3 and the wining path is 3, 8 , 13 ,18,23

Submitted by mf344 on Fri, 06/17/2016 - 12:03

Hi Mohamed. Well done, that sounds right! Can you explain why it works?

Submitted by Sid on Sun, 06/05/2016 - 04:12

Avoid getting the numbers ...

8, 13 and 18. Give the computer 18, and the computer can't do anything to stop your win. If you do get 8 or 13 as the total in your turn, be warned - Unless you're smarter than average, you will be the loser. And also, if the total is 8/13 in the computer's turn, you'll win (if you're smart enough to work out what to do next.)

Submitted by mf344 on Fri, 06/17/2016 - 12:05

Hi there. Looks like you have nearly cracked the strategy. Van you explain it in more detail?

Submitted by gabe on Sun, 06/05/2016 - 16:28

You are the first player

Start with 3. Try to get to 8 then to 13 then to 18 and then you win. 3, 8, 13, 18, 23. Grows by 5. 5 is one more of then you can add.

Submitted by mf344 on Fri, 06/17/2016 - 12:06

That sounds right, well done! Can you explain how this would work for a different target number, and different possible step sizes?

Submitted by nobody on Fri, 06/10/2016 - 08:54

Always start with 3 and try and 18 if you reach 18 the computer cant win!

Submitted by mf344 on Fri, 06/17/2016 - 12:07

Sounds good! Can you explain why that would work?

Submitted by brainbee on Fri, 06/10/2016 - 12:32

You cannot lose if you go to settings and set target number to 10 and highest number to 6.
Start on 3 and no matter what the computer chooses, you will always win!

Submitted by mf344 on Fri, 06/17/2016 - 12:08

True! Can you explain how something similar would work for different settings.

Submitted by Buggie on Fri, 06/10/2016 - 12:53

There is a sequence of numbers to get to.

First, you want 3, then 8, 13, 18 and then you will get to 23.