Question

3. Composition with Red, Blue & Yellow
Ann is a clever painter. Inspired by
Mondrian's work, she decides to create a
mathematical work of art. She divides a
square canvas into 9 equal squares and
paints the central one red. She then
divides each of the 8 remaining
uncoloured squares into 9 equal squares,
painting each of the central squares so
formed yellow. The remaining uncoloured
squares are again each divided into 9, the
centres this time being painted blue. This
process is repeated using a different
colour for each set of central squares until
just over half the original area of the
canvas has been coloured.
How many different colours have then
been used and how many central squares
have been painted?

Answer 1

Ann has used 3 different colors which are: Yellow, Blue and Red, and has drawn a total of 73 center squares on the canvas.

How to calculate the number of central squares that Ann drew?

To calculate the number of central squares that Ann drew we must perform the following operations:

First the canvas was divided into 9 squares and the central one was painted, at this stage we would have 1 central square.

Subsequently, the remaining 8 squares were again divided into 9 squares and the central square was painted to have 8 new central squares.

Additionally, the number of uncolored squares for the next stage must be calculated as shown below:

• 8 × 9 = 72
• 72 - 8 = 64 uncolored squares

Finally, we multiply again to know the total number of squares that we are going to obtain by dividing the uncolored squares by 9 as shown below:

• 64 × 9 = 576

According to the above, to know the total number of painted squares we do the following operation:

• 1 + 8 + 64 = 73 boxes

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