MathDB

2

Part of 1989 Cono Sur Olympiad

Problems(2)

Finf the sum

Source: Cono Sur Olymipiad, Urugay 1989, Problem#2

5/14/2006
Find the sum1+11+111+⋯+111…111⏟n digits.1+11+111+\cdots+\underbrace{111\ldots111}_{n\text{ digits}}.
Constant sum

Source: Cono Sur Olympiad, Uruguay 1989, Problem #5

5/14/2006
Let ABCDABCD be a square with diagonals ACAC and BDBD, and PP a point in one of the sides of the square. Show that the sum of the distances from P to the diagonals is constant.