Week 1 Puzzle: Cicada Survival
This week on The Code, Marcus takes a look at the surprising mathematics behind the mating patterns of the Magicicada. These incredible insects take safety in numbers, emerging at precisely coordinated intervals of 13 or 17 years. By appearing in the hundreds of thousands, the risk to each cicada of being eaten is massively reduced - the predators simply aren’t able to eat the cicadas fast enough to pose a significant threat to the population.
This is a survival strategy known as "predator satiation". The key to this strategy is for the cicadas to emerge in such large numbers. For this to happen, the cicadas must maintain their tightly synchronised life cycles.
It is thought that the primality of these life cycles could be the reason for the survival of these broods of Magicicada. Because the period of their emergence is indivisible, the chances of them appearing at the same time as another brood is greatly reduced. This prevents crossbreeding between broods, which could cause the cicadas to appear at a variety of intervals, vastly reducing their numbers at any given time and increasing the threat presented by predators.
We’ve taken this theory as the inspiration for our puzzle for this week. We want you to imagine an environment which contains four broods of cicadas: A, B, C and D.
Brood A emerges every four years, starting in year four.
Brood B emerges every six years, starting in year six.
Brood C emerges every seven years, starting in year seven.
If a brood’s survival is compromised by emerging in the same year as another brood, what is the shortest life cycle Brood D can have and still survive past year 40?
Enter your answer into the Episode 1 Codebreaker on the ‘fourth hand’. Good luck!