19 October 2019

# A puzzle for the weekend

In a remote part of an African jungle once lived a bunch of lions. No other animal ever came there. Except one day, somehow a deer showed up. Of course, the lions immediately wanted to eat it. Now, these lions were very smart and very courteous. Some might even say they took special “pride” in it 🙂

Puns aside, here are the rules of the puzzle:
(*) the lions have an understanding that only one lion – whoever is first to touch – can kill and eat a deer. (when one attacks, nobody else does; that is where the courteous bit comes in)
(*) they also know that this deer has a property that whichever lion attacks and eats it, itself becomes a deer the next day (which can be attacked and killed by other lions then)
(*) Every lion is desperate to eat a deer. They are okay to live the rest of their life as a deer itself – but will not do so if they know they might get killed the next day by the lions.

Question: Will the deer survive?

Posted October 19, 2019 by Rajib Roy in category "Puzzles

1. By Nitin Thakur on

Does the “lion turning into deer” Cascade? In other words, if lion A eats the deer and turns into a deer, and if lion B eats that deer, (which used to be a lion) would lion B also turn into a dear? If answer is yes, the original deer will not survive

1. By Sri Ganesh on

Nitin Thakur thanks! I was confused. But Rajib Roy is a super specialist so kept mum. I agree to what you say.

2. By Somshekhar Baksi on

Depends on whether the lions’ short-term hunger overpowers their long-term smartness. If it doesn’t, I believe the deer will survive, for the following reason: consider the second-last lion as it is about to eat the deer (which used to be the third-last lion). It knows it will be eaten the next day by the last lion, and will therefore leave the deer alone. Same logic applies all the way back up the chain.
The problem is that no other animal appears in that part of the jungle – so what do the lions eat? This is where hunger comes into play, in which case – oh deer.

3. By Marek Cyzio on

I think the question is incorrect – it should be “how long will it take until lions will go extinct” 😉 Yes, the deer will survive. But lions won’t.

1. By Rajib Roy on

I see how you are thinking but you ask yourself will it get to that point ever?
In any case, the question is will the ORIGINAL deer survive?

2. By Marek Cyzio on

Rajib The way I see it – lions will want to eat the deer. If you assume any lion can catch any deer then the original deer will die and all lions will sequentially convent to deers just to be killed all the way to the last one that will live happily as a deer. Another border case – no lion can catch this deer. Then the deer survives and lions eat vegetables. And then there are cases in between where one of subsequent deers (whose speed by definition doesn’t change) is faster than all remaining lions (who by definition will be the slowest of them all as faster lions already ate a deer and converted).

3. By Marek Cyzio on

It’s interesting that no matter what we can assume about lion performance, we always end up with one deer. But survival of that deer depends only on performance of the best lion.

4. By Roy K. Cherian on

3rd point: …….but will not do so “IF THEY KNOW” they might get killed the next day by the lions. – meaning they might not know?

1. By Roy K. Cherian on

If ‘ALL OF THEM KNOW’ the deer wont get killed. If at least “ANY ONE OF THEM DOESN’T KNOW” the deer will get killed, but only the original Deer.

5. By Marek Cyzio on

It’s interesting that no matter what we can assume about lion performance, we always end up with one deer. But survival of that deer depends only on performance of the best lion.

6. By Abhishek Datta on

Bunch of lions might have died already as no animal ever stepped into that part of the jungle…:( …remaining part is a nice story..:)

1. By Don Mitchell on

I guess the right answer is every line and believes there’s special and won’t be the one that gets eaten and so each of them and turn devour and be devoured

1. By Rajib Roy on

Raghu, By your question, I sense you might have gotten the answer. I just posted it. See if that matches your logic.

7. By Joy A Jensen on

If the lions are truly smart and have survived long enough without eating deer, then the original deer should survive because it would be against any lion’s survival instinct to consume that which could ultimately kill it for a single meal.

1. By Rajib Roy on

It does depend upon the starting number. I just posted the answer – see if this matches your logic.

8. By Rajib Roy on

Solution
Now for the solution. But before that, I have to admit that what was meant to be a simple logic puzzle spawned off some serious lateral thinking about smartness of the lions and such.

Some folks came very close to the answer. It is one of those problems which you prove by using mathematical induction (commonly used in recursive problems).

Let’s start with only one lion (Case 1). Of course, it attacks the deer and eats it. Becomes a deer the next day and happily lives thereafter. The original deer does not survive though.

Case 2: What if there are two lions? Each of the lion is thinking – Well, if I kill the deer and eat it, tomorrow I become deer and the remaining other lion will kill me. So, neither of the lions attack. The deer survives.

Case 3: What if there are three lions? Well, each of the lion will think – If I go for the kill, I become a deer and there are two lions left. It becomes Case 2. No problems. They are not going to kill me. So each lion will try to attack the deer and the first to touch kills it. The deer has no chance of surviving.

Case 4: Now you get the logic. Each lion realizes that if they kill, the next day, they become deer and we have Case 3 in hand. In which case, one of the three remaining lions will surely kill him. So no lion goes forward. The original deer survives.

To generalize, the original deer survives if there are even number of lions and it does not if there are odd number of lions to begin with.

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