This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 2

1973 Bulgaria National Olympiad, Problem 3
Tags: number theory , php
Let $a_1,a_2,\ldots,a_n$ are different integer numbers in the range $[100,200]$ for which: $a_1+a_2+\ldots+a_n\ge11100$. Prove that it can be found at least number from the given in the representation of decimal system on which there are at least two equal digits. [i]L. Davidov[/i]

1998 Croatia National Olympiad, Problem 4
Tags: number theory , php
Among any $79$ consecutive natural numbers there exists one whose sum of digits is divisible by $13$. Find a sequence of $78$ consecutive natural numbers for which the above statement fails.