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Brazilian Mathematical Olympiad N2 (7th-8th grade) Day 1 P2

Source:

November 16, 2018
Brazil

Problem Statement

We say that a quadruple (A,B,C,D)(A,B,C,D) is dobarulho when A,B,CA,B,C are non-zero algorisms and DD is a positive integer such that: 1.1. A≤8A \leq 8 2.2. D>1D>1 3.3. DD divides the six numbers ABC‾\overline{ABC}, BCA‾\overline{BCA}, CAB‾\overline{CAB}, (A+1)CB‾\overline{(A+1)CB}, CB(A+1)‾\overline{CB(A+1)}, B(A+1)C‾\overline{B(A+1)C}. Find all such quadruples.
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