On a square piece of wood with 20 cm sides, a mysterious fellow has painted an interesting design using a brush that is 10 cm wide.
This painter used only one type of paint, but it's quite magical. It starts off pink, as shown in example 1. If the pink is painted over, it turns orange as shown in example 2, and if the orange is painted over, it turns brown as in example 3.
With that in mind, how many brushstrokes did it take to paint this design?
If you think about the colors in order, 1, 2, 3, it's not so tricky. Just be careful not to miss any strokes.
UK Version
If you think about how to build up the required layers by adding brushstrokes in order, it's not too tricky.
Just be careful not to miss out any strokes.
US Version
The painter's first step was painting the entire board pink. How many strokes did this take?
UK Version
A good first step would be to paint the whole board once. Try taking it from there.
US Version
The next step would be to paint the lower left and right corners, which would take two strokes, since you can still see some pink between the two orange parts.
That just leaves the brown part...
UK Version
After painting the whole surface once, you could paint the bottom-left and bottom-right corners with a second layer.
In order to leave the centre free, this requires two strokes.
Now there's just the area with the third coat of paint...
US Version
The two brown sections only took one brush stroke. If this is confusing, remember that painting over the pink paint turns it orange and painting over the orange paint turns it brown.
How many total brushstrokes is that?
UK Version
After painting the board as described in the previous hints, the section with three coats of paint would require just one more brushstroke.
So, how many times was that in total?
Solution
Incorrect
Too bad.
Try thinking through each brushstroke in order.
Correct
Correct!
It took the mysterious fellow only five brushstrokes to paint the design.
Of course, if he didn't have magic paint, it wouldn't be quite so simple.