After a way too long break I finally found the time for a new mathematical quiz on the occasion of my birthday.
Exactly three years ago I celebrated my 25th birthday in the Australian summer. As you all know they have the cutest animals down under: wombats, possums, duckbill platypi and roos. I loved all of them. But most interesting I found a strange breed of chameleons I was able to observe at an outback farm. These chameleons are either black or silver or pink. But they don’t change their color in order to disguise themselves like ordinary chameleons they changed their color according to some strange mechanism.
Whenever two chameleons of different colors snuggle up together they switch to the third color. Like when a black and a siver chameloeon snuggle they both turn pink and so on. When two chameleons have the same color, nothing happens. As these cute little creatures need a lot of love, this mechanism provided a wonderfull natural phenomen. They changed their color back and forth and i was immediately mesmerized. But suddendly i realized that as soon as all chameleons on the farm have the same color they will not be able to change their color anymore. Stricken with fear i counted them. There were 13 black, 15 silver and 17 pink chameleons.
Then I started thinking, if it might be possible that these 45 chameleons all have the same color at some point because they snuggle up in an awkward order. What do you think: Is it possible that this happens – even if it is very unlikely – or is it generally impossible? Please don’t hesitate to ask if you have anymore questions. I am looking forward to your answers and your arguments.
Full of love and numbers, your
Photos by Sabine Reitmaier