A pair of newborn male and female rabbits is placed in an enclosure to breed. The rabbits start to bear young ONE MONTH after their own birth. At the end of each month, they have another male-female pair, which in turn mature and start to bear young ONE MONTH later. None of the rabbits die. How many rabbits will there be at the end of SIX MONTHS from the start?
End of month 1: 2 pair
Month 2: 4 pair
Month 3: 8 pair
Month 4: 16 pair
Month 5: 32 pair
Month 6: 64 pair = 128 rabbits
To solve this problem, let's break down the rabbit population growth month by month:
Month 1:
- We start with a pair of newborn male and female rabbits.
Month 2:
- The original pair matures and produces another pair of rabbits.
Month 3:
- The original pair reproduces again, bringing the total population to (1 original pair) + (1 new pair) = 2 pairs of rabbits.
Month 4:
- The original pair produces another pair, and the second pair from Month 2 also reproduces for the first time. This brings the total population to (2 pairs from Month 3) + (1 new pair) = 3 pairs of rabbits.
Month 5:
- The original pair reproduces again, the second pair from Month 2 produces their second pair, and the third pair from Month 3 reproduces for the first time. This brings the total population to (3 pairs from Month 4) + (1 new pair) + (1 new pair) = 5 pairs of rabbits.
Month 6:
- The original pair produces another pair, the second pair from Month 2 produces their second pair, the third pair from Month 3 produces their first pair, and the fourth pair from Month 4 reproduces for the first time. This brings the total population to (5 pairs from Month 5) + (1 new pair) + (1 new pair) + (1 new pair) = 8 pairs of rabbits.
Since each pair of rabbits consists of a male and a female, we can count the total number of rabbits by multiplying the number of pairs by 2:
Total number of rabbits at the end of 6 months = 8 pairs * 2 rabbits per pair = 16 rabbits.
Therefore, at the end of six months, there will be a total of 16 rabbits in the enclosure.