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You have nine identically looking coins, one of which is counterfeit and weighs less than the original. You also have three balance scales $-$ two of which work properly and …

Suppose you have a balance and an unknown weight of $m \text{ kg}$, such that $100 ≥ m > 0$. If you are allowed to craft a weight of any …

On an island, everyone is either a knight or a knave. Knights only tell the truth (only make true statements), and knaves always lie (only make false statements).

There exists …

Let $P$ be an arbitrary property such that the following holds for all natural numbers $k$.

If $P$ holds for all natural numbers smaller than $k$, then $P$ holds for …

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