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ASU 468 All Soviet Union MO 1988 blackboard game (m and n)=> m+n+mn

Source:

August 7, 2019
combinatoricsalgebra

Problem Statement

The numbers 11 and 22 are written on an empty blackboard. Whenever the numbers mm and nn appear on the blackboard the number m+n+mnm + n + mn may be written. Can we obtain :
(1) 1312113121,
(2) 1213112131?