In this POW, we had to figure out how fast two rats populated a deserted island with no other animals/dangers on it. The two rats, once they arrived on the island, had a litter of six baby rats, and had another litter of six every 40 days until they died. Every female rat on the island mated and had babies 120 days after its birth, and had litters of six every 40 days thereafter. Every litter was evenly spread with male and female rats, and no one died during the first year. The goal was to find how many rats would be on the island after one year.
What I did first for this problem was visually mapped out the rats that would be born in each generation. My method, while a little unorganized, made sense to me, and got me thinking really critically about the problem. The one thing I didn’t do was get the right answer. I had failed to count the biggest generation of rats - the last one, born from the babies of the second generation.
After that, I refined my method of organization, and made an even more useful, efficient, graph. This one took into account all of the rats that were born in every generation, which made it really easy to see how many rats there were that were going to be born in the generation 120 days later.
Unfortunately, though I knew what the right answer was - 1,808 rats - I was never able to reach it. I ran into some complications with the amount of rats to add per generation, starting with day 240, and continuing from there. Every time I tried to decide on a logical way to go, it turned out to be wrong. In the end, I ended up with 1,592 rats. If I were to do this problem again, I would definitely have made sure much earlier I knew how many rats to add per generation.
The Habits of a Mathematician that I used during this problem were visualize, because of how I chose to solve it, and keep organized, for the same reason. My way of organizing my thoughts was really effective for keeping my brain on the thinking track of the problem.
What I did first for this problem was visually mapped out the rats that would be born in each generation. My method, while a little unorganized, made sense to me, and got me thinking really critically about the problem. The one thing I didn’t do was get the right answer. I had failed to count the biggest generation of rats - the last one, born from the babies of the second generation.
After that, I refined my method of organization, and made an even more useful, efficient, graph. This one took into account all of the rats that were born in every generation, which made it really easy to see how many rats there were that were going to be born in the generation 120 days later.
Unfortunately, though I knew what the right answer was - 1,808 rats - I was never able to reach it. I ran into some complications with the amount of rats to add per generation, starting with day 240, and continuing from there. Every time I tried to decide on a logical way to go, it turned out to be wrong. In the end, I ended up with 1,592 rats. If I were to do this problem again, I would definitely have made sure much earlier I knew how many rats to add per generation.
The Habits of a Mathematician that I used during this problem were visualize, because of how I chose to solve it, and keep organized, for the same reason. My way of organizing my thoughts was really effective for keeping my brain on the thinking track of the problem.