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After years of experiments, you've finally created the pets of the future -- nano-rabbits!
经过数年的实验，你终于创造出了未来宠物--纳米兔子！
They're tiny, they're fuzzy... and they multiply faster than the eye can see.
它们很小且毛茸茸的...它们繁殖的速度快到肉眼看不见。
In your lab there are 36 habitat cells, arranged in an inverted pyramid, with 8 cells in the top row.
在你的实验室里，有36间“孵化小屋”，以倒金字塔形式排列，最上面一层有8间。
The first has one rabbit, the second has two, and so on, with eight rabbits in the last one.
第1间有一只兔子，第2间有2只兔子，以此类推，最后一间有8只兔子。
The other rows of cells are empty... for now.
其它层的"小屋"都是空的--目前是空的。
The rabbits are hermaphroditic, and each rabbit in a given cell
这些兔子雌雄同笼，在每一间中的每一只兔子，
will breed once with every rabbit in the horizontally adjacent cells, producing exactly one offspring each time.
都会与横向隔壁间的兔子交配一次，每次都生出一只新兔子。
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.
新生出来的兔子会直接落到父母住处正下方的那件“小屋”，在几分钟之内就会长大，可以换它们开始交配。
Each cell can hold 10^80 nano-rabbits -- that's a 1 followed by 80 zeros -- before they break free and overrun the world.
每一间“小屋”可以容纳10^80只纳米兔子--也就是是1后面加80个0--超过这个数字的话，他们就会逃出“小屋”，占领世界。
Your calculations have given you a 46-digit number for the count of rabbits in the bottom cell -- plenty of room to spare.
你通过计算，得出在最低下的“小屋”中兔子的个数只有46位数--空间绰绰有余。
But just as you pull the lever to start the experiment, your assistant runs in with terrible news.
但当你拉动操作杆要开始实验时，你的助理带着坏消息跑来。
A rival lab has sabotaged your code so that all the zeros at the end of your results got cut off.
你竞争对手的实验室破坏了你的程序代码，所以你最后算出的结果其实最后面的0都被切掉了。
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!
那就表示你其实不知道最下面的“小屋”是否能容纳所有的兔子--但繁殖已经开始了！
To make matters worse, your devices and calculators are all malfunctioning, so you only have a few minutes to work it out by hand.
更糟糕的是，你的设备和计算器都出故障了，你只有几分钟的时间手动计算。
How many trailing zeros should there be at the end of the count of rabbits in the bottom habitat?
最底层小屋中兔子的数量应该含有多少个0？
And do you need to pull the emergency shut-down lever?
你需要去拉动紧急关闭的控制杆吗？
There isn't enough time to calculate the exact number of rabbits in the final cell.
我们没有足够的时间算出最后一间小屋中的兔子数目。
The good news is we don't need to. All we need to figure out is how many trailing zeros it has.
好消息是，我们并不需要算出它。我们只需要算出后面有多少个0。
But how can we know how many trailing zeros a number has without calculating the number itself?
但我们怎么能在不计算出这个数目的情况下知道后面有几个0呢？
What we do know is that we arrive at the number of rabbits in the bottom cell through a process of multiplication -- literally.
我们只知道，底层小屋的兔子数目是经过相乘运算得到的--字面意义。
The number of rabbits in each cell is the product of the number of rabbits in each of the two cells above it.
每间小屋的兔子数目是上面两间小屋中的兔子数目相乘。
And there are only two ways to get numbers with trailing zeros through multiplication:
只有两种方法可以透过乘法得到后面有0的数字：
either multiplying a number ending in 5 by any even number, or by multiplying numbers that have trailing zeroes themselves.
把尾数是5的数字和任何偶数相乘，或是将本身尾数就是0的数字相乘。
Let's calculate the number of rabbits in the second row and see what patterns emerge.
让我们来算一下第二层的兔子数目，看看会发现什么规律。
Two of the numbers have trailing zeros -- 20 rabbits in the fourth cell and 30 in the fifth cell.
有两个数字的尾数有0--第4间有20只兔子，第5间有30只。
But there are no numbers ending in 5.
没有尾数是5的数字出现。
And since the only way to get a number ending in 5 through multiplication is by starting with a number ending in 5,
因为若要透过乘法得到尾数是5的数字，一定要用尾数是5的数字来乘，
there won't be any more down the line either.
因此可确定下面也不会出现尾数是5的数字。
That means we only need to worry about the numbers that have trailing zeros themselves.
那就表示：我们只需担心本身末尾是0的数字。
And a neat trick to figure out the amount of trailing zeros in a product
有个小妙招可以知道乘积的尾数有几个0，
is to count and add the trailing zeros in each of the factors -- for example, 10 x 100 = 1,000.
那就是算出每个因数尾数的0有几个，再将再们相加--比如，10×100=1000。
So let's take the numbers in the fourth and fifth cells and multiply down from there.
所以，我们从第二排第4、第5间的数目着手开始向下相乘。
20 and 30 each have one zero, so the product of both cells will have two trailing zeros,
20和30尾数都有1个0，所有这两间相乘尾数会有2个0，
while the product of either cell and an adjacent non-zero-ending cell will have only one.
这两间小屋和其隔壁数目尾数非0，小屋相乘得到的乘积尾数只有1个0。
When we continue all the way down, we end up with 35 zeros in the bottom cell.
我们继续向下计算，会算出在最底层小屋中的兔子数目尾数有35个0。
And if you're not too stressed about the potential nano-rabbit apocalypse,
如果你不太担心纳米兔可能带来的灾难，
you might notice that counting the zeros this way forms part of Pascal's triangle.
你可能会注意到用这种方式计算0会形成杨辉三角形。
Adding those 35 zeros to the 46 digit number we had before yields an 81 digit number -- too big for the habitat to contain!
将那35个0加在我们之前算出的46位数字后面得到一个81位数数字--超出小屋的容量！
You rush over and pull the emergency switch just as the seventh generation of rabbits was about to mature -- hare-raisingly close to disaster.
你跑过去，拉下紧急开关，此时第7代兔子刚要长大--差一点点就要发生大灾难了。
