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

The different colours that has been used is red, yellow and blue and the number of central squares is = 73 boxes

The Mondrian's work

The First division that was divided into 9 equal parts has = 1 coloured red.

The second division is 8 remaining

uncoloured squares into 9 equal squares = 8×9= 72boxes

The number of boxes that was coloured yellow =8 boxes

The remaining uncolored boxes which is = 72 - 8 = 64 boxes

The third division is the division of each remaining uncolored boxes into 9. That is 64 × 9 = 576

The number of boxes that was coloured blue = 64 boxes

Therefore the number of central squares that has been coloured = 1 + 8 + 64

= 73 boxes

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