Figuring out circuit with correct power

[Teszla]

You have a Voltage source of 12 V, three 6V-lamps with 18W and three 6V-lamps with 12W.

How can you connect five of the lamps with the voltage source to make all five have correct power?

I understand that the voltage drop across each lamp must be 6 V, which means that there must be maximum two elements in series. But other than that, how can we determine how the circuit should look? It seems like it can only be done by guessing and trying different setups until we find one that works?

My question is, is there any methodological way of finding out how the circuit should look, that is not based on guessing?

 

[E-design]

What is important is for the total wattage over each series section (where a section can be a number of lamps connected in parallel) to be the same in order to split the power evenly.
One way is to write an equation where you put the power of the number of parallel 12W lamps equal to the power of the number of 18W parallel lamps.
Get the ratio and you can work out how many lamps of each type need to be connected.

You can also solve these two equations :
12x = 18y
x+y = 5

Which will give you; x=3 and y=2

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You can even solve it graphically if you want by plotting the two equations.