I was watching a Japanese game show.

enter image description here

The contestants were asked to find the black area.

I could tell that the black area was half of the overall area. However, the contestants said that

The alignment of this figure was based on some rules.

He does not said what rules was it nor mention that it was simply half black half white.

I might be overthinking this, but I was pretty curious whether there was such rule or not...

EDIT: Again, I can see that the area was half black half white. However, I just want to know if there is a well-known rule or pattern that fits this type of alignment.

  • 1
    $\begingroup$ Not sure what rules are intended, but it's easy to see that it's half-black: consider each of the three wedges (arrow shapes jutting out of a black line) to be made of two triangles, and move those two triangles to appear at each end of the line instead of jutting out. Then divide the black triangle which is second from the top-left into two smaller ones, and put those two at the end of the bottom-right black strip. Now the resulting picture is manifestly half black. $\endgroup$ – Patrick Stevens Feb 17 '18 at 10:11
  • $\begingroup$ So how could you tell that the black area was half of the overall area? $\endgroup$ – Bram28 Feb 17 '18 at 13:15
  • $\begingroup$ This is more a matter of English and Japanese, so I'm not sure if I'm interpreting the Japanese (or your intent) wrong, but the word used at 3:06 in that video is 規則性, which dictionaries suggest is more like "regularity", rather than something as concrete as a "rule". $\endgroup$ – Mark S. Feb 17 '18 at 14:16

Take the black triangles as shown (in red) here:


Move them to the edges as shown here:


Now it is obvious that the coloured bits take up exactly one half of the big square.


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