An Engaging Rabbit Puzzle and Its Solution
Among the most famous and intriguing puzzles in the “logical brain teasers” category is the rabbit problem. The premise is as follows: Imagine you have a pair of rabbits that produce a new pair of bunnies each month. These new pairs of bunnies in turn become capable of reproducing after one month. Now, here’s the challenge: How many pairs of rabbits will there be in half a year (six months)?
The correct answer is 21 pairs of rabbits. Let’s break down how to arrive at this number.
There are several ways to solve this problem. One of the simplest methods involves sequentially adding the number of rabbit pairs each month. Let’s examine this month by month:
1. In the first month, we have one pair of rabbits.
2. In the second month, another pair of rabbits appears, making it two pairs in total.
3. In the third month, the first pair produces a new pair of bunnies, while the second pair just starts reproducing, totaling three pairs.
4. In the fourth month, the first pair produces another new pair, and the second pair also gives birth to a new pair, resulting in five pairs overall.
And so on. We observe that with each subsequent month, the number of rabbit pairs increases significantly due to their prolific nature.
An even more fascinating fact: this problem is closely linked to the Fibonacci sequence. In this sequence, each number is the sum of the two preceding numbers (1, 1, 2, 3, 5, 8, 13, 21, etc.). Remarkably, the number of rabbit pairs after N months corresponds to the N-th number in the Fibonacci sequence. For example, after four months, the number of rabbit pairs corresponds to the fifth number in the sequence, which is 5.
Using the Fibonacci sequence not only simplifies the calculations but also makes the rabbit problem exceptionally captivating. Armed with this method, you can easily tackle more complex variations of this puzzle by simply referring to the appropriate number in the Fibonacci sequence. Try figuring out how many pairs of rabbits there will be in a year, or even two years! You just need to find the corresponding number in the sequence!
