Tiger and Sheep

How it works

The story sets three facts: a hundred tigers and one sheep share a magic island with nothing but grass; tigers would rather eat the sheep, but any tiger that does instantly becomes a sheep itself; and every tiger is perfectly rational and above all wants to survive. Then the question: with 100 tigers on the island, will the sheep be eaten?

Clicking through takes you to the answer builder at /brain-teasers/tiger-and-sheep/answer. You pick a tiger count - the choices are 1 through 8, then 100 - predict whether the sheep gets eaten or is safe, and write out your reasoning. A narrated walkthrough lives at /brain-teasers/tiger-and-sheep/breakdown.

How scoring works

Your prediction is checked against the exact rule the code computes: the sheep is eaten if and only if the tiger count is odd. A wrong prediction shows you the correct outcome for the count you picked.

Your explanation is scanned for five key ideas by transparent keyword matching: tigers are rational, survival comes first, eating turns the tiger into a sheep, the reasoning works through the smaller (n - 1) case, and the odd/even pattern is noticed. Plain wording that names those concepts is what registers.

Shrink the island before you reason about it

One hundred tigers is unmanageable directly; one tiger is trivial. With a single tiger, eating is free - there is no other tiger left to eat it after it transforms - so the sheep is eaten. That is the base case, and the whole puzzle is the discipline of starting there instead of at 100.

With two tigers, each one reasons: if I eat, I become the only sheep on an island with one hungry tiger, and the one-tiger case just told me that sheep gets eaten. So neither tiger eats, and the sheep is safe. Every larger case is built by exactly this move.

A tiger eats only if the island it creates is safe

The decision rule that drives the induction: eating turns an n-tiger island into an (n - 1)-tiger island with the eater as the sheep. A rational, survival-first tiger eats exactly when that (n - 1)-tiger island is safe for its sheep. Safe islands are the even ones, so tigers eat when n is odd - making odd islands deadly - and hold back when n is even.

State the conclusion as a rule, not a story: eaten if and only if n is odd. With 100 tigers, the count is even, every tiger knows eating would make it the sheep on a deadly 99-tiger island, and the sheep grazes untouched.

In the builder, walk the ladder in order

The count picker offering 1 through 8 before 100 is the intended path. Predict each small case, check it, and the alternating pattern shows itself by n = 3 or 4. Then 100 is not a new problem - it is the pattern plus one sentence of justification.

When you write the explanation, use the words the checklist is listening for: rational, survive, becomes a sheep, the n - 1 case, odd and even. Those are also precisely the words an interviewer needs to hear.

A worked example

Pick 3 tigers in the builder. Base case: 1 tiger eats, sheep eaten. 2 tigers: eating would leave the eater as the sheep with 1 tiger - deadly - so no one eats, sheep safe.

3 tigers: a tiger that eats becomes the sheep on a 2-tiger island, which the previous step showed is safe. So eating is safe, some tiger does it, and the sheep is eaten. Predict 'sheep gets eaten' - correct. The rule is now visible: eaten when odd, safe when even. For 100 tigers, even, predict 'sheep is safe' and write the induction in two sentences.

Common mistakes

• Answering '100 hungry tigers, of course it gets eaten' - the transformation rule makes eating a personal risk, and instinct ignores it.

• Starting the reasoning at 100 instead of 1. The argument only assembles from the base case upward.

• Getting the parity backwards - re-derive the small cases rather than recalling which of odd or even was safe.

• Forgetting that all tigers share the same reasoning. The argument needs every tiger to be rational and to know the others are, and dropping that assumption breaks the chain.

• Writing a vague explanation. The grader and interviewers alike are listening for the n - 1 step and the odd/even rule stated explicitly.

Why interviews test this

This is a standard induction teaser: the interviewer is testing whether you instinctively reduce an intractable number to a base case, build a recurrence, and state the resulting invariant cleanly. The 100 in the problem is a bluff - candidates who engage with it directly, rather than with n = 1, have already missed the point.