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13 Mondrian

© Frauke Jansen, MATH+

Author: Cor Hurkens (TU Eindhoven)
Project: 4TU.AMI

Challenge

Mondrian, the painter-elf, has designed a square-shaped Christmas card and has divided it into 121 square-shaped cells in an 11×11 pattern (see Fig. 1a). Mondrian paints little stars into three of the cells exactly as shown in Figure 1a.

Then, Mondrian partitions the remaining grid of 118 cells into several 1×2 and 2×1 rectangles (each containing 2 cells), and 2×2 squares (each containing 4 cells) that he paints with bright colors (see Fig. 1b). In the end, each of the 118 cells belongs to exactly one such rectangle or square. The three cells with the little stars are not covered.

Figure 1a: Mondrian’s Christmas card with the three little stars.

Figure 1b: Example: Mondrian’s Christmas card with two rectangles and one square.

What is the largest possible number of 2×2 squares that Mondrian can paint onto his Christmas card?

Possible answers:

  1.  The largest possible number of 2×2 squares is 14.
  2.  The largest possible number of 2×2 squares is 15.
  3.  The largest possible number of 2×2 squares is 16.
  4.  The largest possible number of 2×2 squares is 17.
  5.  The largest possible number of 2×2 squares is 18.
  6.  The largest possible number of 2×2 squares is 19.
  7.  The largest possible number of 2×2 squares is 20.
  8.  The largest possible number of 2×2 squares is 21
  9.  The largest possible number of 2×2 squares is 22.
  10.  The largest possible number of 2×2 squares is 23.