MathDB
Four digit numbers

Source: Archimedes Junior 2013

March 16, 2020
combinatorics

Problem Statement

Let A=abcd‾A=\overline{abcd} be a four-digit positive integer with digits a,b,c,da, b, c, d, such that a≥7a\ge7 and a>b>c>d>0a>b>c>d>0. Consider the positive integer B=dcba‾B=\overline{dcba} , that comes from number AA by reverting the order of it's digits. Given that the number A+BA+B has all it's digits odd, find all possible values of number AA.
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