Mathematical and Physical Journal
for High Schools
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Problem A. 573. (November 2012)

A. 573. Let D={0,1,2,...,9} be the set of decimal digits, and let R\subsetD×D be a set of ordered pairs of digits. An infinite sequence (a1,a2,a3,...) of digits is said to be compatible with R if (aj,aj+1)\inR for all positive integer j. Determine the smallest positive integer K with the property that if an arbitrary set R\subsetD×D is compatible with at least K distinct digit sequences then R is compatible with infinitely many digit sequences.

Based on the 5th problem of CIIM 2012, Guanajuato, Mexico

(5 pont)

Deadline expired on December 10, 2012.


15 students sent a solution.
5 points:Ágoston Péter, Fehér Zsombor, Janzer Olivér, Maga Balázs, Omer Cerrahoglu, Vályi András, Williams Kada, Zilahi Tamás.
4 points:Herczeg József, Ioan Laurentiu Ploscaru.
2 points:2 students.
1 point:1 student.
0 point:2 students.

Problems in Mathematics of KöMaL, November 2012