1
Part of 2012 CentroAmerican
Problems(2)
700 times the sum of its digits
Source: Centroamerican 2012, Problem 1
6/19/2012
Find all positive integers that are equal to times the sum of its digits.
sum of digitsnumber theoryCentroamericandigit sum
Intersections of lines in equilateral triangle
Source: Centroamerican 2012, Problem 4
6/20/2012
Trilandia is a very unusual city. The city has the shape of an equilateral triangle of side lenght 2012. The streets divide the city into several blocks that are shaped like equilateral triangles of side lenght 1. There are streets at the border of Trilandia too. There are 6036 streets in total. The mayor wants to put sentinel sites at some intersections of the city to monitor the streets. A sentinel site can monitor every street on which it is located. What is the smallest number of sentinel sites that are required to monitor every street of Trilandia?
floor functioncombinatorics unsolvedcombinatorics