Q2 BT: Tiger and Sheep
Brain teaser number two from the book “A Practical Guide to Quantitative Finance Interviews” by Zhou Xinfeg.
Question statement
One hundred tigers and one sheep are put on a magic island that only has grass. Tigers can eat grass, but they would rather eat sheep. Assume: (A). Each time only one tiger can eat one sheep, and that tiger itself will become a sheep after it eat the sheep. (B). All tigers are smart and perfectly rational and they want to survive. So will the sheep be eaten?
Assumptions
- Each time only one tiger can eat sheep.
- A tiger will become a sheep after it eats the sheep.
- All tigers are smart and perfectly rational: They want to survive.
- The tiger that eats a sheep its the whole sheep. There is no “meat sharing”.
- Tigers have two food sources: grass and sheep.
Solution and explanation
The question is if the sheep will be eaten. Lets reduce make it simpler by reducing the number of tigers down to one.
1 tiger, 1 sheep
It’ll definitely eat the sheep. There’s no fear that after it becomes a sheep, itll be eaten. There won’t be tigers left to do that after it turns.
2 tigers, 1 sheep
The sheep won’t be eaten since each will be afraid they’d be next in line for being eaten by the tiger that does not turn into a sheep.
3 tigers, 1 sheep
The sheep will be eaten. One tiger will eat the sheep well knowing the remaining two won’t dare to eat it. From the previous example we know that in a scenario where there’s two tigers and 1 sheep the sheep ain’t eaten for the previously provided explanation.
4 tigers, 1 sheep
The sheep will stay alive. All tigers will be afraid of becoming the sheep that will certainly be eaten as per the reasons stated in the 3 tigers, 1 sheep scenario.
The pattern
Whenever there’s an even number of tigers, the sheep is safe. Otherwise, the sheep gets eaten.
That’s it for this one.