19. As shown in the figure, it is composed of four overlapping rectangles, with eight small circles at the intersection points. Please fill in the eight natural numbers 1,2,3,4,5,6,7,8 into these small circles so that the sum of the four numbers on each rectangle is equal.
This one wants a proof. Work it on paper, read the official solution, then mark
yourself honestly — the ladder only means something if the record is true.
Official solution
Answer:
Translate the text above into English, please retain the original text's line breaks and format, and output the translation result directly.
Source: NuminaMath-1.5,
licensed Apache-2.0.
Statement and solution reproduced as published; topic, difficulty and ordering added
by this site.