Red and Blue Bacteria
Source: Problem 1, Brazilian MO, 2012
November 28, 2012
functionprobabilitycombinatorics unsolvedcombinatorics
Problem Statement
In a culturing of bacteria, there are two species of them: red and blue bacteria.When two red bacteria meet, they transform into one blue bacterium.
When two blue bacteria meet, they transform into four red bacteria.
When a red and a blue bacteria meet, they transform into three red bacteria.Find, in function of the amount of blue bacteria and the red bacteria initially in the culturing,
all possible amounts of bacteria, and for every possible amount, the possible amounts of red and blue bacteria.