Have you got it?

Can you explain the strategy for winning this game with any target?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

Have You Got It? printable sheet



Have You Got It? is an adding game for two players. You can play against the computer or with a friend. It is a version of a well known game called Nim.

Start with a target of 23.

The first player chooses a whole number from 1 to 4.

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.

Play the game several times.

Can you find a winning strategy?

Can you always win?

Does your strategy depend on whether or not you go first?

 

Tablet/Full Screen Version

 

 



To change the game, choose a new target or a new range of numbers to add.

Test out the strategy you found earlier. Does it need adapting?

Can you work out a winning strategy for any target?

Can you work out a winning strategy for any range of numbers?

Is it best to start the game? Always?

Away from the computer, challenge your friends:

One of you names the target and range and lets the other player start.

Extension:

Can you play without writing anything down?

Consider playing the game where a player CANNOT add the same number as that used previously by their opponent.

You may want to take a look at Last Biscuit, a more demanding game which requires similar strategic thinking.

Click here for a poster of this problem.