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Logic lab

Ordering Guards

Listen to who speaks and what they reveal about their neighbors.

The question

Four guards stand in a line. Each guard either always speaks or always stays silent. When questioned, the visitor hears:

Which guards are the speakers and which stay silent?

Hints

The speaking guards only tell the truth, so their statements describe what is actually happening.

Answer

Guards 2 and 4 must be the silent ones because they never say anything. Guard 3 claims that Guard 4 is silent, which is true, so Guard 3 must speak. Guard 1 insists he is not the only speaker, which is also true since Guard 3 speaks as well. Therefore Guards 1 and 3 are the speakers, and Guards 2 and 4 stay silent.