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← Punched Cards & a Lights Puzzle

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Lesson 4 of 7

Five lights, one answer

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7 min

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Five lamps stand in a row. Each is ON or OFF. A setting is the state of all five lamps. Which setting is it?

32 cards, one for each setting.
Step 1 of 6
  1. 32 cards, one for each setting.
  2. Clue: lamp 5 is ON. 16 cards left.
  3. Clue: lamps 4 and 5 are the same. 8 left.
  4. Clue: lamps 3 and 4 are different. 4 left.
  5. Clue: lamps 2 and 3 are the same. 2 left.
  6. Clue: lamps 1 and 2 are different. 1 left.

The rule

Each clue keeps only the settings that obey it. When one setting is left, that is the answer.

Five lamps make 32 settings, because each lamp doubles the list. Put one setting on each card.

Write a setting as five marks: ON, OFF or X. X means the lamp can be ON or OFF. The clue "lamp 5 is ON" is X X X X ON. It keeps 16 cards, because four X marks make 16 patterns. Each X has 2 choices. So 2 × 2 × 2 × 2 = 16.

A clue about two lamps, like "same", also keeps half the cards. Two lamps can be set 4 ways. Exactly 2 of them are the same. In this puzzle each clue keeps half of the cards still showing. Five clues leave one.

Switch on clues to leave 4 cards. Then leave 1.

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