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Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?


Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3


The game Got It is a version of a well known old favourite called Nim.
It is an adding game for two. You play against the computer or against a friend.

Start with a target of $23$. Set the range of available numbers 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.

Play the game several times. Can you always win?
Can you find a winning strategy?

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

Change the game, choose a new GOT IT! target.

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

Can you work out a winning strategy for any target?

Is it best to start the game? Always?

Change the game again, returning to a target of $23$ but using a different range of numbers this time.

Test out the strategies you found earlier. Do they need adapting?

Can you work out a winning strategy for any range of numbers? Is it best to start the game? Always?

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


Can you play without writing anything down?

Target $24$ using either a $1$, $3$ or $5$. What is the strategy now?

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

Play NIM.


Students might be:

Thinking strategically in a puzzling context
Devising winning ways
Following through on insights gained
Exploring the notions of complements.