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Cuisenaire Environment

An environment which simulates working with Cuisenaire rods.

Square It

Age 11 to 16
Challenge Level

Modbury School sent us some ideas for this activity.

Will said:

Make a triangle with a hollow middle, then fill the middle dot in the top line and wait for the computer to make its desicion.

I think you mean like this:

Then go in the opposite position,
You win, every time you decide you want to win.

George said:

Our soloution is to go three across one down in the centre of your three and when your other opponent goes for one of the squares you will always have another square to go to.

I think you mean something that looks like this:

Yes, that's a very good strategy as it means there are three possible squares to make with your next move (can you see where the three are?).

Hannah said:

You can count the squares that you can make using each point. Then, you should always choose the dots which can make the most squares.

That's all you need to do to know all of them because the grid is symmetrical.

Naima said:

If you go first, you can be in control of the game, because you can always make 3 corners of a square so that the computer is forced to choose the 4th point.

You should choose points that make squares with as many of your other points as possible. Once you can make two different squares then you know you will win.

Here are my examples. I start in the middle because that dot can make the most squares.

I didn't want to let the computer control the game by having 3 corners of the yellow square, so I chose the corner of the yellow square that gave me 3 corners of a square.

I chose the point that makes 3 corners of the red square and 3 corners of the blue square, so I knew I would win.

Second example:

I drew squares to help decide where to go to make 3 corners of a square. It's good to choose a point that gives you lots of opportunities to make more squares. By choosing 3 corners of the pink square, you either have 2 corners of the green square and the black square, or you have 2 corners of the red square and the blue square. I wasn't sure which was better so I drew the squares the computer could make for each one.

The computer can make more squares if it goes at the top of the pink square, so I chose that one.

If I choose blue point 4, the computer has to choose red 4 so I can't make the red square. But then I can choose point 5 and then I've made 3 corners of the blue square and the black square, so I can win.

Thank you all who were involved at Modbury, we hope to hear from you again.