3-ча 5. Given twenty cards. Each digit from zero to nine inclusive is written on two of these cards (only one digit on each card). Can the cards be arranged in a row so that the zeros stand next to each other, there is exactly one card between the ones, two cards between the twos, and so on up to the nines, between which there should be nine cards?
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
Solve 5.
\section*{Third Round}
\section*{8th Grade}
Source: NuminaMath-1.5,
licensed Apache-2.0.
Statement and solution reproduced as published; topic, difficulty and ordering added
by this site.