Weihnachtsmann rot

Challenge from 1. December

Mondrian

Authors: , Hajo Broersma, Cor Hurkens

Project: 4TU.AMI

Challenge:

Mondrian, the painter-elf, has designed a square-shaped Christmas card and has subdivided it into 100 square-shaped cells in a 10 x 10 pattern, as shown in Figure 1.

Figure 1: Mondrian's unfinished Christmas card

Furthermore, Mondrian has drawn 30 black circles on his card. Around each of these 30 black circles, Mondrian has constructed a painted region; the blue region, the green region, and the yellow region are shown in picture 1.

  • Each painted region consists of one or more cells of the 10 x 10 pattern.

  • Each cell belongs to exactly one region.

  • The cells of each region are connected: You can reach every cell of the region from every other cell of the region, by making a sequence of horizontal and vertical steps within the region.

  • The regions do not contain holes.

  • Every region contains exactly one connected black circle in its interior. No additional circular segments are allowed in a region.

  • Every region is rotationally symmetric: If you rotate the region by 180 degrees around its black circle, then the rotated region coincides with the original region.

Here are some examples of such rotationally symmetric regions with a black circle as its center:


Question: What is the area of the largest region on Mondrians finished Christmas card (cf. Fig. 1)?


Artwork: Julia Nurit Schönnagel

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Possible answers:

  1. The largest region consists of 9 cells.

  2. The largest region consists of 10 cells.

  3. The largest region consists of 11 cells.

  4. The largest region consists of 12 cells.

  5. The largest region consists of 13 cells.

  6. The largest region consists of 14 cells.

  7. The largest region consists of 15 cells.

  8. The largest region consists of 16 cells.

  9. The largest region consists of 17 cells.

  10. The largest region consists of 18 cells.

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