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Got It for Two

Age 7 to 14 Challenge Level:

Here’s a game to play with an adult! It is a version of a well known game called Nim.


How do you play?
You'll need an adult to play with.
You will also need some paper to write down the numbers on, or you could use the interactive version here.
Start with the Got It target $23$. The adult chooses a whole number from $1$ to $4$. Then take turns to add a whole number from $1$ to $4$ to the running total. The person who hits the target of $23$ wins the game. Play the game several times, swapping who goes first. To change the game, choose a new Got It target or a new range of numbers to add on.

Can you find a winning strategy?
Can you always win?
Does your strategy depend on whether or not you go first?
When is it better to go first and when is it better to let the grown-up go first?
Can you work out a winning strategy for any target?
Can you work out a winning strategy for any range of numbers?
Notes for adults
This game helps children to practise simple addition and subtraction. However, the real challenge is to find a winning strategy that always works and this involves working systematically, conjecturing, refining ideas, generalising and using knowledge of factors and multiples.

Easier version: have a lower target and a shorter range of numbers (e.g. $10$, using $1$ and $2$). Note down running totals.
Harder version: play without writing anything down, or play a variation where a player cannot add the same number as that used previously by the opponent.

Repeat the game, aiming to find a winning strategy, then talk together about how it was found.

There's a classroom version of this game here.