three lions and three wildebeest flee for their lives.

三頭獅子和三隻角馬逃命四竄

To escape the inferno,

為了逃脫煉獄

they must cross over to the left bank of a crocodile-infested river.

他們必須渡過有鱷魚棲息其中的河畔

Fortunately, there happens to be a raft nearby.

幸運的是，附近剛好有艘竹筏

It can carry up to two animals at a time,

一次能承載兩隻動物

and needs at least one lion or wildebeest on board to row it across the river.

而且來回都需要至少有一隻動物把船開回來

There's just one problem.

這裡就只有一個問題

If the lions ever outnumber the wildebeest on either side of the river,

不論河的哪一端，如果獅子的數量多過角馬

even for a moment, their instincts will kick in, and the results won't be pretty.

哪怕只要一秒，牠們便會野性衝腦，結果將會不太妙

That includes the animals in the boat when it's on a given side of the river.

包括當竹筏上在著兩隻獅子到只有一隻角馬在的彼岸也是一樣

What's the fastest way for all six animals to get across without the lions stopping for dinner?

那最快讓六隻動物都順利渡河且沒有讓獅子有空停留下來享用晚餐的最少渡河次數是多少呢？

Pause here if you want to figure it out for yourself.

你若想要自己想答案的話就按暫停

Answer in: 3

答案會在：3 秒後公布

Answer in: 2

答案會在：2 秒後公布

Answer in: 1

答案會在：1 秒後公布

If you feel stuck on a problem like this,

你如果感到困在這種問題當中的話

try listing all the decisions you can make at each point,

試著將所有可能性列出來

and the consequences each choice leads to.

然後看有哪些選項會帶你往目標邁進

For instance, there are five options for who goes across first:

舉例來說，第一步有五個選擇：

one wildebeest,

一隻角馬渡河

one lion,

一頭獅子渡河

two wildebeest,

兩隻角馬

two lions,

兩隻獅子

or one of each.

或各一隻

If one animal goes alone,

如果一隻動物單獨渡河

it'll just have to come straight back.

就必須在把竹筏開回來

And if two wildebeest cross first,

而如果兩隻角馬先過河

the remaining one will immediately get eaten.

剩下的那隻就會馬上被吃掉

So those options are all out.

所以那些選項都被刪掉了

Sending two lions,

剩下兩頭獅子先過

or one of each animal,

或各一隻先過

can actually both lead to solutions in the same number of moves.

都能夠以同樣的步數來解決這個問題

For the sake of time, we'll focus on the second one.

因為時間的關係，我們會專注在第二個選擇

One of each animal crosses.

各一隻動物先過河

Now, if the wildebeest stays and the lion returns,

現在，如果讓角馬留在對岸然後獅子回頭

there will be three lions on the right bank.

就會形成三隻獅子在右岸

Bad news for the two remaining wildebeest.

對剩下兩隻角馬來說可是壞消息

So we need to have the lion stay on the left bank

所以我們需要留一頭獅子在左岸

and the wildebeest go back to the right.

然後讓角馬把竹筏開回去

Now we have the same five options,

現在我們有同樣的五個選項

but with one lion already on the left bank.

但當一頭獅子已經在左岸

If two wildebeest go, the one that stays will get eaten,

如果這時兩隻角馬渡河，右岸那隻角馬就會被吃了

and if one of each animal goes,

而若是兩種動物各一隻渡河

the wildebeest on the raft will be outnumbered as soon as it reaches the other side.

渡河的角馬在一到左岸的時候就會寡不敵眾

So that's a dead end,

所以這是條死路

which means that at the third crossing,

也就是說在第三次渡河

only the two lions can go.

就只有一種選擇，就是讓兩頭獅子過去

One gets dropped off,

一頭留在左岸

leaving two lions on the left bank.

現在就有兩頭獅子在左岸

The third lion takes the raft back to the right bank

第三隻獅子就把竹筏開回右岸

where the wildebeest are waiting.

去接剩下在等待的角馬們

What now?

那現在怎麼做？

Well, since we've got two lions waiting on the left bank,

嗯，因為左岸現在有兩頭獅子

the only option is for two wildebeest to cross.

唯一的選擇就只有待兩隻角馬過河

Next, there's no sense in two wildebeest going back,

然後，沒有理由做白工地再把兩隻角馬帶回來

since that just reverses the last step.

因為這就是重複上一個動作而已

And if two lions go back,

而若兩頭獅子回來

they'll outnumber the wildebeest on the right bank.

在右岸剩下的一隻角馬就會被吃

So one lion and one wildebeest take the raft back

所以一頭獅子和一隻角馬一起從左岸回來

leaving us with one of each animal on the left bank

讓兩邊的動物都達到數量上的平衡

and two of each on the right.

左岸各一隻，右岸各兩隻

Again, there's no point in sending the lion-wildebeest pair back,

一樣地，再將獅子-角馬對移回左岸也是沒意義的

so the next trip should be either a pair of lions

所以下一趟不是兩頭獅子就是

or a pair of wildebeest.

一對角馬過河

If the lions go, they'd eat the wildebeest on the left, so they stay,

如果獅子對過河，左岸角馬就會被吃，所以牠們留下

and the two wildebeest cross instead.

而兩頭角馬先過河

Now we're quite close because the wildebeest are all where they need to be with safety in numbers.

現在我們快要完成了，因為角馬都安全地到達左岸

All that's left is for that one lion to raft back

再來就是如何將竹筏開回去接剩下的獅子

and bring his fellow lions over one by one.

一頭一頭地將牠們運過河

That makes eleven trips total,

總共會花十一趟

the smallest number needed to get everyone across safely.

這就是讓大家安全過河所需花費最少的趟數

The solution that involves sending both lions on the first step works similarly,

這個解法與當初第一趟將兩頭獅子運過河的形式是相似的

and also takes eleven crossings.

也都需花費十一趟

The six animals escape unharmed from the fire just in time

六頭動物毫髮無傷地及時渡河

and begin their new lives across the river.

展開牠們在彼岸的新生活

Of course, now that the danger's passed,

當然，現在當危險過去

it remains to be seen how long their unlikely alliance will last.

這樣的不太可能的聯盟關係會持續多久沒人知道