# Hungry lions and a goat

There are 53 lions in a cage and 1 goat. All the lions are very hungry and would want to eat the goat. But the problem here is that any lion who eats the goat can satisfy his hunger but he will himself become a goat and then other lions will eat him. All lions are intelligent and understand this fact, so obviously no one wants to die becoming a prey for others.

So, the question here is will the goat be eaten or not?

• Since the goat is not atomic, and it isn't defined what happens if some lions "share" the goat, chances are high it won't be eaten. Because if two lions each eat one half of the goat, will there be 51 hungry lions and two goats, or 53 lions and not a single goat? Ah, and what happens if a lion eats a lion? – Alexander Oct 4 '14 at 17:41
• Of course, a lion could eat a lion, couldn't it? – Florian F Oct 6 '14 at 7:32
• This all assumes the lions don't mind becoming goats! That is a big assumption. I don't think your average lion is cool with becoming a goat. – ThePopMachine Oct 6 '14 at 18:02
• Some of the answers show that a more strictly defined priority list over what the lions value would be helpful in the question. 1: Not being eaten 2: Eating a goat. This leaves less room for people to use non-deduction along the lines of "they would eat goats out of desperation despite certainty of death if they do". Saw a version having "lions can survive off eating the infinitely available grass, but prefer eating goats" as well, which was a nice touch. – Jakob Pamp Bengtsson Jul 25 '17 at 9:26

Let's follow the usual approach for this.

Say there's just 1 lion and the goat. Would the lion eat the goat? Yes, it's not at risk.

So say there's 2 lions and a goat. Would a lion eat the goat? If so it would become the goat in the 1 lion and a goat situation, and so it would be eaten. So it would not eat the goat.

If there's 3 lions and a goat, would a lion eat the goat? Well there'd be 2 left, and as we just worked out, with 2 left, the goat is safe.

So it becomes clear that the pattern is: odd number of lions, goat gets eaten, even number, goat is safe. So with 53, the goat gets eaten.

• perfect answer. – Harryom Oct 4 '14 at 0:06
• @Harryom Not for the goat. – JakeGould Oct 4 '14 at 6:13
• So in the cases where there are more than one lion, which one eats the goat? – sebastian-c Oct 4 '14 at 21:44
• @sebastian-c Don't think it's possible to say, but I also don't see any way that could affect the answer to the actual question – Ben Aaronson Oct 4 '14 at 21:47
• I still think the goat would get eaten in either case. One of the lions would kill the other lions first and then eat the goat. It is the only logical outcome that prevents the individual lion from dying through either starvation or getting eaten. – Willem Oct 5 '14 at 12:29

If you think of 53 as just a large number, you might first believe the goat is at risk of being eaten.

But then you see that if a lion eats the goat, it becomes the goat among a large number of lions and will just as likely be eaten. The lions would therefore rather be the last lion to eat the goat. As a result, none will try to eat the goat first.

If that is the case, that means the goat is safe.

But if a goat is safe among many lions, it should be safe for a lion to eat the goat.

The solution

You have to understand that the situation is very different between 53 and 52 lions. To understand why, you have to consider each number separately.

1. With 1 goat against 1 lion, the goat gets eaten. Obviously.
2. With 1 goat against 2 lions, if a lion eats the goat it becomes 1 goat against 1 lion and gets eaten. No lion wants that, so the goat survives.
3. With 1 goat against 3 lions, if a lion eats the goat it becomes 1 goat against 2 lions and survives. So the goat gets eaten by the fastest lion.
4. With 1 goat against 4 lions, if a lion eats the goat it becomes 1 goat against 3 lions and gets eaten. No lion wants that so the goat survives.

You can see a general pattern emerging:

• With an even number of lions, if a lion eats the goat it becomes 1 goat against an odd number of lions and gets eaten. So the goat survives.
• With an odd number of lions, if a lion eats the goat, it becomes 1 goat against en even number of lions and suvives. So the goat gets eaten.

Since we have an odd number of lions, the goat gets eaten by the fastest lion. The lion becomes a goat and from there on it survives with all 52 lions.

• I just realized Ben Aaronson was faster then my. Damn. – Florian F Oct 4 '14 at 6:24
• I really prefer this explanation, it's much more clear what's going on. I was still confused after reading Ben's answer, so please keep this one around. – Adam Davis Oct 4 '14 at 12:34
• This answer explains it much better than the accepted answer. – Keavon Oct 5 '14 at 7:08
• This answer is more perfect and clearer than the accepted answer. Anyhow I up-voted both answers ;-) – Sathiya Kumar Oct 5 '14 at 9:45
• And yet, it is exactly the same explanation. – Florian F Oct 6 '14 at 7:26

The goat will be eaten by all the lions because all of them are very hungry. If they don't eat anything at all, they'll die anyway. So as the lions are intelligent, they wouldn't like to die with an empty stomach.

The solution?

• The goat is eaten by the first lion (which is impatient). Then that lion becomes a goat.

• The second lion eats that goat and itself becomes a goat.

• And so on...

In this way, every lions satisfies his hunger. The last lion among them (which is the most intelligent and patient of the pack) will eat the last goat (i.e. the second last lion) and will become a goat.

The point?

The point here is that the LAST lion becomes the survivor and is transformed into a goat. Now he has to eat veg for the rest of his life, and if he won't then he will also die. The lions need to fill their stomachs. Period.

The number of lions doesn't matter for this problem. Whether there're 53 lions or 53000, it's the same.

• The question is tagged with logical-deduction, ordinary realistic reasoning does not apply. "The lions will eat the goat because they're hungry" is an additional rule not stated in the question. – Jakob Pamp Bengtsson Jul 25 '17 at 9:29