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As a wildfire rages through the grasslands, three lions and three wildebeest flee for their lives.
一场大火席卷了草原，三头狮子和三只牛羚正在逃命。
To escape the inferno, they must cross over to the left bank of a crocodile-infested river.
为了逃离这场大火，它们必须渡过一条潜伏着鳄鱼的小河。
Fortunately, there happens to be a raft nearby.
幸运的是，附近恰好有一个小木筏。
It can carry up to two animals at a time,
它一次可供最多两只动物渡河。
and needs as least one lion or wildebeest on board to row it across the river. There's just one problem.
但每次至少有一只动物控制小木筏渡河。只有一个问题。
If the lions ever outnumber the wildebeest on either side of the river,
一旦河的任何一边狮子的数量多于牛羚，
even for a moment, their instincts will kick in, and the results won't be pretty.
即使只是很短的时间，狮子也会因本能而攻击牛羚。
That includes the animals in the boat when it's on a given side of the river.
小木筏上的动物将会同时算在河的两边。
What's the fastest way for all six animals to get across without the lions stopping for dinner?
那么，这六只动物怎样才能最快地渡河，并且牛羚不会被狮子所攻击？
If you feel stuck on a problem like this,
如果你认为毫无头绪，
try listing all the decisions you can make at each point, and the consequences each choice leads to.
可以试着在纸上列举出所有时刻的每一种的可能性以及它们所导致的后果。
For instance, there are five options for who goes across first:
比如，第一次渡河有五种选择：
one wildebeest, one lion, two wildebeest, two lions, or one of each.
一只牛羚，一头狮子，两只牛羚，两头狮子，或者每种一只。
If one animal goes alone, it'll just have to come straight back.
如果第一次让一只动物渡河，那么它只能原路返回。
And if two wildebeest cross first, the remaining one will immediately get eaten.
而如果让两只牛羚渡河，那么剩下的一只牛羚就会立刻被吃掉。
So those options are all out.
所以这些选择是行不通的。
Sending two lions, or one of each animal, can actually both lead to solutions in the same number of moves.
要么先让两头狮子渡河，要么让一头狮子和一只牛羚渡河，这两种选择后各自又产生了五种可能性。
For the sake of time, we'll focus on the second one. One of each animal crosses.
由于时间的关系，我们直接看第二种。先让每种动物各一只渡河。
Now, if the wildebeest stays and the lion returns, there will be three lions on the right bank.
然后，如果让牛羚待在对岸让狮子返回，那么一边就会有三头狮子。
Bad news for the two remaining wildebeest.
剩下的两只牛羚就性命难保了。
So we need to have the lion stay on the left bank and the wildebeest go back to the right.
所以我们需要让狮子待在对岸，让牛羚返回。
Now we have the same five options, but with one lion already on the left bank.
现在我们又有同样的五种选择，但是对岸已经有一头狮子了。
If two wildebeest go, the one that stays will get eaten,
如果同时让两只牛羚渡河，剩下的一只就会被吃掉，
and if one of each animal goes, the wildebeest on the raft will be outnumbered as soon as it reaches the other side.
如果每种动物各取一只，那么小木筏上的牛羚在到达对岸时就会被吃掉。
So that's a dead end, which means that at the third crossing, only the two lions can go.
这两种方法又被排除掉了，也就是说第三次渡河只能让两只狮子同时渡河。
One gets dropped off, leaving two lions on the left bank.
然后在对岸放下一只，对岸就有两头狮子。
The third lion takes the raft back to the right bank where the wildebeest are waiting.
第三头狮子独自返回，原来的一边还是有三只牛羚。
What now? Well, since we've got two lions waiting on the left bank,
现在怎么办？既然我们已经让两头狮子到达了河对岸，
the only option is for two wildebeest to cross.
唯一的选择就是让两只牛羚过去。
Next, there's no sense in two wildebeest going back, since that just reverses the last step.
然后，由于让这两只牛羚直接返回是毫无意义的，也就是重复了上一步。
And if two lions go back, they'll outnumber the wildebeest on the right bank.
而如果让两只狮子同时返回，又会导致狮子的数量多于牛羚。
So one lion and one wildebeest take the raft back
所以只能各取一只返回，
leaving us with one of each animal on the left bank and two of each on the right.
河对岸每种动物各有一只，原来的一边每种动物各有两只。
Again, there's no point in sending the lion-wildebeest pair back,
同理，让每种动物各一只再次渡河又会重复上一步骤，
so the next trip should be either a pair of lions or a pair of wildebeest.
所以现在只能让两头狮子渡河，或者让两只牛羚渡河。
If the lions go, they'd eat the wildebeest on the left, so they stay, and the two wildebeest cross instead.
如果让两头狮子渡河，他们会立即吃掉对岸的牛羚，所以只能让两只牛羚渡河。
Now we're quite close because the wildebeest are all where they need to be with safety in numbers.
现在我们已经胜利在望了，因为三只牛羚都到达了河对岸。
All that's left is for that one lion to raft back and bring his fellow lions over one by one.
只需要再让剩下的一头狮子上船，然后每次带着一只狮子渡河即可。
That makes eleven trips total, the smallest number needed to get everyone across safely.
这样一共需要十一步，也就是所有动物渡河所需的最少步骤。
The solution that involves sending both lions on the first step works similarly, and also takes eleven crossings.
如果第一步将两头狮子送往河对岸，最后也能以类似的方式解决这一问题，同样需要十一步。
The six animals escape unharmed from the fire just in time and begin their new lives across the river.
六只动物及时逃离了危险，并在河的对岸开始了新的生活。
Of course, now that the danger's passed, it remains to be seen how long their unlikely alliance will last.
当然，既然危险已经过去，他们的合作关系还能否继续呢？
