Published May 2004,February 2011.
This article gives you a few ideas for understanding the game and how you might find a winning strategy. The aim is not to give you an answer but to unpick the problem in such a way that if you meet similar games in the future you might be able to work out winning strategies for them too.
The game can be found on the site.
Start with the Got It target 23.
The first player chooses a whole number from 1 to 5.
Players take turns to add a whole number from 1 to 5 to the running total.
The player who hits the target of 23 wins the game.
Here is an example of a game played between two friends, Jo goes first and chooses 5:
Jo 
Chris 
Running Total 
5 

5 

4 
9 
2 

11 

5 
17 
3 

20 

3 
23 Chris wins! 
To change the game, you can choose a new Got It target or a new range of numbers to add on.
Are you good at mental arithmetic? Can you play without writing anything down?
Is it better to go first or second?
What is the winning strategy?
If you are still not sure, have a go against the computer.
Can one player guarantee winning? Are the winning strategies similar?
Should you go first or second?
Does the same strategy work?
Should you go first or second?
Think carefully about the winning strategy that you found when the target number changed, but your choice of numbers was 1, 2 , 3, 4 or 5.
Your strategy probably included the number 6. Why?
Try to explain your strategy to a friend. This could help you to understand your strategy better, which will help you with the next challenge.
Explain your strategy.
When should you go first and when should you go second?
We have suggested games with a smaller range of numbers first because starting small often helps to understand the challenge better.
Try games with a choice of 1 or 2. Play the game with different target numbers. You may want to try playing with targets of 5, 7, 19 and 21.
Try games with a choice of 1, 2 or 3. Play the game with different target numbers. You may want to try playing with targets of 5, 6, 19 and 32.
Explain your strategy.
When should you go first and when should you go second?
Hopefully this article has helped you to find a strategy which will work for any target number, and any range of numbers. Now you can dazzle your friends!
Challenge your friends. Ask your friend to name the target and range, and play the game. If you are able to choose whether you go first or second, you should always be able to win the game.
But can your friends work out how?