Henry Ernest Dudeney/Puzzles and Curious Problems/284 - Lamp Signalling

Puzzles and Curious Problems by Henry Ernest Dudeney: $284$

Lamp Signalling

Two spies on the opposite sides of a river devised a method for signalling by night.

They each put up a stand, like the diagram, and each had three lamps which could show either white, red or green.

They constructed a code in which every different signal meant a sentence.

Note that a single lamp on any one of the hooks could only mean the same thing,

that two lamps hung on the upper hooks $1$ and $2$ could not be distinguished from two on, for example, $4$ and $5$.

However, two red lamps on $1$ and $5$ could be distinguished from two on $1$ and $6$,

and two on $1$ and $2$ from two on $1$ and $3$.

Remembering the variations of colour as well as of position, what is the greatest number of signals that could be sent?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Combination and Group Problems: $284$. -- Lamp Signalling
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Miscellaneous Combinatorial Puzzles: $463$. Lamp Signalling