Can you solve the river crossing riddle

你能解決過河之謎嗎

來源視頻

As a wildfire rages through the grasslands, three lions and three wildebeest flee for their lives.

To escape the inferno, they must cross over to the left bank of a crocodile-infested river.

Fortunately, there happens to be a raft nearby.

It can carry up to two animals at a time, and needs as least one lion or wildebeest on board to row it across the river.

一場(chǎng)大火席卷了草原三頭獅子和三只牛羚正在逃命

為了逃離這場(chǎng)大火他們必須渡過一條潛伏著鱷魚的小河

幸運(yùn)的是，附近恰好有一個(gè)小木筏

一次可供最多兩只動(dòng)物渡河,但每次至少有一只動(dòng)物控制小木筏渡河

There's just one problem.

If the lions ever outnumber the wildebeest on either side of the river, even for a moment, their instincts will kick in, and the results won't be pretty.?

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

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

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

Answer in: 3?

Answer in: 2?

Answer in: 1

只是有一個(gè)問題

一旦河的任何一邊?獅子的數(shù)量多于牛羚，即使只是很短的時(shí)間，獅子也會(huì)因本能而攻擊牛羚

小木筏上的動(dòng)物將會(huì)同時(shí)算在河的兩邊

那么?這六只動(dòng)物怎樣才能最快地渡河？并且牛羚不會(huì)被獅子所攻擊

（可以暫停視頻?思考一下這個(gè)問題）

（3秒后公布答案）

（2秒后公布答案）

（1秒后公布答案）

If you feel stuck on a problem like this, try listing all the decisions you can make at each point, and the consequences each choice leads to.?

For instance, there are five options for who goes across first: one wildebeest, one lion, two wildebeest, two lions, or one of each.?

If one animal goes alone, it'll just have to come straight back.

And if two wildebeest cross first, the remaining one will immediately get eaten.?

So those options are all out.

如果你認(rèn)為毫無頭緒，可以試著在紙上列舉出 所有時(shí)刻的每一種的可能性，以及它們所導(dǎo)致的后果

比如 第一次渡河有五種選擇，一只牛羚，一頭獅子，兩只牛羚，兩頭獅子或者每種一只

如果第一次讓一只動(dòng)物渡河，那么它只能原路返回

而如果讓兩只牛羚渡河，那么剩下的一只牛羚就會(huì)立刻被吃掉

所以現(xiàn)在只剩下兩種可能

Sending two lions, or one of each animal, can actually both lead to solutions in the same number of moves.?

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

One of each animal crosses.?

Now, if the wildebeest stays and the lion returns, there will be three lions on the right bank.

Bad news for the two remaining wildebeest.?

So we need to have the lion stay on the left bank and the wildebeest go back to the right.

要么先讓兩頭獅子渡河，要么讓一頭獅子和一只牛羚渡河，這兩種選擇后 各自又產(chǎn)生了五種可能性

由于時(shí)間的關(guān)系 ，我們直接看第二種

先讓每種動(dòng)物各一只渡河

然后 如果讓牛羚待在對(duì)岸 讓獅子返回，那么一邊就會(huì)有三頭獅子

剩下的兩只牛羚就性命難保了

所以我們需要讓獅子待在對(duì)岸讓牛羚返回

Now we have the same five options, but with one lion already on the left bank.

If two wildebeest go, the one that stays will get eaten, and if one of each animal goes, the wildebeest on the raft will be outnumbered as soon as it reaches the other side.?

So that's a dead end, which means that at the third crossing, only the two lions can go.

One gets dropped off, leaving two lions on the left bank.?

The third lion takes the raft back to the right bank where the wildebeest are waiting.?

What now?

現(xiàn)在我們又有同樣的五種選擇，但是既然對(duì)岸已經(jīng)有一頭獅子

如果同時(shí)讓兩只牛羚渡河 ，剩下的一只就會(huì)被吃掉，如果每種動(dòng)物各取一只，那么小木筏上的牛羚在到達(dá)對(duì)岸時(shí)就會(huì)被吃掉

這兩種方法又被排除掉了也就是說 第三次渡河只能讓兩只獅子同時(shí)渡河

然后在對(duì)岸放下一只，對(duì)岸就有兩頭獅子

第三頭獅子獨(dú)自返回原來的一邊還是有三只牛羚

現(xiàn)在怎么辦？

Well, since we've got two lions waiting on the left bank, the only option is for two wildebeest to cross.?

Next, there's no sense in two wildebeest going back, since that just reverses the last step.

And if two lions go back, they'll outnumber the wildebeest on the right bank.?

So one lion and one wildebeest take the raft back leaving us with one of each animal on the left bank and two of each on the right.

Again, there's no point in sending the lion-wildebeest pair back, so the next trip should be either a pair of lions or a pair of wildebeest.?

If the lions go, they'd eat the wildebeest on the left, so they stay, and the two wildebeest cross instead.

既然我們已經(jīng)讓兩頭獅子到達(dá)了河對(duì)岸，唯一的選擇就是讓兩只牛羚過去

然后 由于讓這兩只牛羚直接返回是毫無意義的，也就是重復(fù)了上一步

而如果讓兩只獅子同時(shí)返回，又會(huì)導(dǎo)致獅子的數(shù)量多于牛羚

所以只能各取一只返回，河對(duì)岸每種動(dòng)物各有一只，原來的一邊每種動(dòng)物各有兩只

同理 讓每種動(dòng)物各一只再次渡河，又會(huì)重復(fù)上一步驟，所以現(xiàn)在只能讓兩頭獅子渡河或者讓兩只牛羚渡河

如果讓兩頭獅子渡河， 他們會(huì)立即吃掉對(duì)岸的牛羚，所以只能讓兩只牛羚渡河

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

All that's left is for that one lion to raft back and bring his fellow lions over one by one.?

That makes eleven trips total, the smallest number needed to get everyone across safely.

The solution that involves sending both lions on the first step works similarly, and also takes eleven crossings.

The six animals escape unharmed from the fire just in time and begin their new lives across the river.

Of course, now that the danger's passed, it remains to be seen how long their unlikely alliance will last.

現(xiàn)在 我們已經(jīng)勝利在望了，因?yàn)槿慌Ａ缍嫉竭_(dá)了河對(duì)岸

只需要再讓剩下的一頭獅子上船，然后每次帶著一只獅子渡河即可

這樣一共需要十一步，也就是所有動(dòng)物渡河所需的最少步驟

如果第一步將兩頭獅子送往河對(duì)岸 ，最后也能以類似的方式解決這一問題，同樣需要十一步

六只動(dòng)物及時(shí)逃離了危險(xiǎn)，并在河的對(duì)岸開始了新的生活

當(dāng)然 ，既然危險(xiǎn)已經(jīng)過去他們的合作關(guān)系還能否繼續(xù)呢？