You have 6 coins of distinct weights and a beam balance with two pans. You devise an algorithm that identifies the **second lightest** coin with complete certainty with at most \(M\) weighings.

What is the minimum possible value of \(M?\)

Consider trying this problem first.

On an **infinitely large** chess board, is there a configuration of kings and knights such that each king attacks exactly 2 kings and 2 knights, and each knight attacks exactly 2 kings and 2 knights?

This problem is part of the new Brilliant.org Open Problems Group (see Open Problem #1).

Call a non-empty set \(\mathbb V\) of non-zero integers *victorious* if there exists a polynomial \(P(x)\) with integer coefficients such that \(P(0) = 330\) and \(P(v) = 2|v|\) for all elements \(v \in \mathbb V.\)

How many *victorious* sets exist?

×

Problem Loading...

Note Loading...

Set Loading...