three numbers with the same digits
Source: All-Russian olympiad 1995, Grade 9, Second Day, Problem 5
October 21, 2013
number theory proposednumber theory
Problem Statement
We call natural numbers similar if they are written with the same (decimal) digits. For example, 112, 121, 211 are similar numbers having the digits 1, 1, 2. Show that there exist three similar 1995-digit numbers with no zero digits, such that the sum of two of them equals the third.
S. Dvoryaninov