Can you solve the multiplying rabbits riddle? - Alex Gendler

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After years of experiments, you've finally created the pets of the future, nanorabbits. They're tiny, they're fuzzy, and they multiply faster than the eye can see. In your lab, there are 36 habitat cells arranged in an inverted pyramid, with eight cells in the top row. The first has one rabbit, the second has two, and so on, with eight rabbits in the last one. The other rows of cells are empty, for now. The rabbits are hermaphroditic, and each rabbit in a given cell will breed once with every rabbit in the horizontally adjacent cells, producing exactly one offspring each time. the newborn rabbits will drop into the cell directly below the two cells of its parents, and within minutes, will mature and reproduce in turn. Each cell can hold 10 to the 80th power nanorabbits— that's a one followed by 80 zeros— before they break free and overrun the world. Your calculations have given you a 46-digit number for the count of rabbits in the bottom cell— plenty of room to spare. But just as you pull the lever to start the experiment, your assistant runs in with terrible news. A rival lab has sabotaged your code so that all the zeros at the end of your results got cut off. That means you don't actually know if the bottom cell will be able to hold all the rabbits, and the reproduction is already underway. To make matters worse, your devices and calculators are all malfunctioning, so you only have a few minutes to work it out by hand. How many trailing zeros should there be at the end of the count of rabbits in the bottom habitat? And do you need to pull the emergency shutdown lever? But there isn't enough time to calculate the exact number of rabbits in the final cell. The good news is we don't need to. All we need to figure out is how many trailing zeros it has. But how can we know how many trailing zeros a number has without calculating the number itself? What we do know is that we arrive at the number of rabbits in the bottom cell through a process of multiplication, literally. The number of rabbits in each cell is the product of the number of rabbits in each of the two cells above it. And there are only two ways to get numbers with trailing zeros through multiplication, either multiplying a number ending in 5 by any even number, or by multiplying numbers that have trailing zeros themselves. Let's calculate the number of rabbits in the second row and see what