PROBLEM 4. We say that a number of the form $\overline{0, a b c d e}$ has property $(P)$ if the digits $a, b, c, d, e$ belong to the set $\{4,6\}$.

a) Show that the solution to the equation $x+0,46646=1,1111$ has property $(P)$;

b) Determine how many different numbers of the form $\overline{0, a b c d e}$ have property $(P)$;

c) Show that from any 17 different numbers of the form $\overline{0, a b c d e}$ that have property $(P)$, two can be chosen whose sum is 1,1111 .[^0]

## NATIONAL MATHEMATICS OLYMPIAD  Local stage - 5.03. 2016  GRADING GUIDE - 6th Grade