Hello everyone! I hope you are having a good day, anyways your day is going to get even better because you have the honor to learn about the Wheat Seed Problem today.

It is a mathematical riddle from stochastics (statistics) which asks the question “what is the likelyhood of a wheat population to ever go extinct?”

Let me introduce the basics: You are a farmer and start out with a single wheat seed. When you plant a seed into the ground, it grows into a wheat plant, which you can harvest. Harvest gives you anything from 0 to 3 (inclusive) new wheat seeds, which you can then plant again next year.

Let me show you an illustration:

(Icons from Mineclonia, https://codeberg.org/mineclonia/mineclonia)

Obviously, when you run out of seeds, you have nothing to replant the next year; The population goes extinct and the game is over.

The question is: What is the likelyhood of that never happening? In other words, what is the likelyhood that you can continue to plant seeds year after year, until infinity?

The probability for each plant (when harvested) are: 25% that it gives you 0, 1, 2, or 3 seeds each. That means that on average, you get 1.5 new seeds per plant, so you get more than you invested. This means that the average size of your population goes up with time.

However, whenever the population reaches 0 seeds in total at any one year, then the game is lost.

What is the chance that you can continue to plant new plants each year indefinitely?

solution

I will post the solution in a follow-up post. Think about it yourself first :)