Gurmeet.Net
Puzzles

## Twelve Coins

### Puzzle

One of twelve coins is counterfeit: it is either heavier or lighter than the rest. Is it possible to identify the counterfeit coin in three weighings on a beam balance?

### Source

Classic puzzle that I first encountered in 1993-1994 time frame.

### Solution

Several excellent expositions of various approaches:

Previous Puzzle: My Cap Color

At the Secret Convention of Logicians, the Master Logician placed a band on each attendee's head, such that everyone else could see it but the person themselves could not. There were many, many different colours of band. The Logicians all sat in a circle, and the Master instructed them that a bell was to be rung in the forest at regular intervals: at the moment when a Logician knew the colour on his own forehead, he was to leave at the next bell. Anyone who left at the wrong bell was clearly not a true Logician but an evil infiltrator and would be thrown out of the Convention post haste; but the Master reassures the group by stating that the puzzle would not be impossible for anybody present. How did they do it?

Next Puzzle: Grid Infection

In an n by n grid of squares, two squares are neighbors if they share an edge. Initially, some squares are "infected". At successive clock ticks, an uninfected square gets infected if at least two of its neighbors are infected. How many squares must initially be infected so that all squares eventually get infected?