[MathManTG]

This problem was solved in slightly different form back in 1202 by Leonardo Fibonacci, giving rise to the Fibonacci numbers, one of the most wonderful things in all of mathematics.It's fairly complicated to work out exact numbers, but what it comes down to is exponential growth.The numbers you give are explosive, so the percentage increase is huge.Each pair produces 15 kittens per year, 7.5 times as many as you start with, or 750 %.Let's say they wait a full year instead of 6 months to start.At the end of year 2, they have added 15.At the end of year 3, they have added another 15,and the first 15 have added 112.5 (never mind what .5 cats means or the fact that it is an odd number).At the end of year 4, another 15, another 112.5, and 843.75 on top of that.At the end of year 5, ANOTHER 15, 112.5, 843.75 + 6328.125.You can see where this is headed.These numbers are not exact, because they do everything year by year rather than every 4 or 6 months,but it gives an idea of how fast exponential growth is.They also don't take into account that eventually the cats stop reproducing. As long as births exceed deaths, the numbers keep going up.The human population is increasing by "just" 3% per year, nowhere near 750%, and you can see how many of us there are.For perhaps a more realistic set of numbers, instead of increasing by 7.5 times, use "only" 3 or 4.If each pair produces 6 kittens instead of 15,2, 2+6, 2+6+24, 2+6+24+96, 2+6+24+96+384 = (2, 8, 32, 128, 512)With 8 kittens instead of 15,2, 2+8, 2+8+40, 2+8+40+200, 2+8+40+200+1000 = (2, 10, 50, 250, 1250...)