MEMO 2016 ekipno problem 7


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 6,0
Dodao/la: arhiva
29. kolovoza 2018.
LaTeX PDF

A positive integer n is called a Mozartian number if the numbers 1, 2, \ldots , n together contain an even number of each digit (in base 10).

Prove:

(a) All Mozartian numbers are even.
(b) There are infinitely many Mozartian numbers.

Izvor: Srednjoeuropska matematička olimpijada 2016, ekipno natjecanje, problem 7