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Part of 2014 CentroAmerican

Problems(2)

Source: Centroamerican Olympiad 2014, problem 1

A positive integer is called tico if it is the product of three different prime numbers that add up to 74. Verify that 2014 is tico. Which year will be the next tico year? Which one will be the last tico year in history?

number theoryprime numbersnumber theory proposed

Figures with at most 2014 squares

Source: Centroamerican Olympiad 2014, problem 4

Using squares of side 1, a stair-like figure is formed in stages following the pattern of the drawing.
For example, the first stage uses 1 square, the second uses 5, etc. Determine the last stage for which the corresponding figure uses less than 2014 squares.
http://www.artofproblemsolving.com/Forum/download/file.php?id=49934

combinatorics proposedcombinatorics