Tag Archives: Combinations

138. Kandinsky Combinations!

This week I gave a talk to a group of PGCE/Schools Direct associates about innovation and ‘keeping it fresh’. One of my points was you should ‘Keep the good ideas and bin the rubbish/pointless ones’. This is one of my ideas I kept – first used in the late 1990s!

Wassily Kandinsky was an artist, born in Russia in 1866. He died in France in 1944. He is credited with being the first artist to explore purely abstract work. Researching him is a nice homework task which can add to the final work.

Farbstudie quadrate mit konzentrischen ringen


This work has been reproduced thousands of times -you can see it everywhere from student bedrooms to upmarket coffee shops. The original was completed in 1913. It roughly translates as colour study squares with concentric circles.


You will need:
Squared paper (or plain)
Coloured pencils or pens

1. Show the class the painting and discuss how the colours are arranged.

2. How many ways can you colour in one square with one colour? 1

3. How many ways can you colour in two concentric squares with two colours? 2

4. Repeat for three colours and ask for predictions. The usual prediction is 3, the answer is 6.

5. Repeat the process and ask them if they can see a pattern forming. Encourage them to be methodical.

The colour patterns form a set of factorial numbers. Finding out about factorials could be a good extension task.

After the work is completed you’ve potentially got a great wall display, a cross-curricular link to art and an understanding of combinations/factorials.

This also looks rather cool done with concentric equilateral triangles or hexagons on isometric paper.

23. Coffee overload

I was sat in a coffee shop when I overheard the barista say to a customer ‘Take your time, there are about 20,000 different drinks available’.

Sounded like a mathematical challenge to me.


If the menu below was real, how many different drinks could made?

How many would be drinkable?

Size: S, M, L

Drink: Filter, Americano, Cappucinno, Machiatto, Latte, Espresso, Hot chocolate.

Coffee type: Decaf or caffeinated

Flavour: Vanilla, Mint, Hazelnut, Ginger, Caramel, None

Milk: None, whole, skimmed, soya

Hint: Be methodical, work out the hot chocolate options first.

Hot choc
Size *Flavour*Milk = 3*6*4 = 72

Size*Drink*Type*Flavour*Milk =
3*6*2*6*4 = 864

Total number of drinks
864 + 72 = 936

This doesn’t consider extra shots of coffee or syrup. Imagine how many variations there are in a big coffee shop!

Me … I’ll have a black filter, no milk, no sugar.